Disclaimer: For unusual situations that aren't specifically covered; however, of which existing rules can be applied, read below.
Two-Fisted Abe
If Two-Fisted Abe is simply trying to touch him, then yes of course, roll a touch attack. This would be no different from a spell caster rolling a touch attack. The only difference is, nothing happens after the touch.
It should even work with weapons. Not every attack roll has to be met with brute force.
Something similar can be seen in the movie Kingdom of Heaven; the Knight Hospitaller taps Balian on the head with his sword. He didn't cause any damage. He didn't try to penetrate armor. But he was making a point.
What is the mechanic used? A touch attack. It is in the definitions. Tell the DM, "I want to touch him to show him that I can hit him and not cause any damage." Remember Armor Class is not really hit or miss. A failure to do damage on an attack roll probably did in fact hit the opponent (hit is touch AC) but you failed to penetrate his armor, or his agility, or his other defenses (shield, natural armor, etc). A roll of a 1 is an automatic miss, because you fail to hit even his touch AC.
One-Shot Bill
If One-Shot Bill is simply trying to lob an arrow without causing damage, then he can't do that with his bow. The bow sends the projectile outward and if the arrow does damage, it does damage.
A GM could make a house rule that such a master with a bow could launch an arrow with just the right amount of draw that the arrow bounces off - but that is so unlikely it would have to be a -10 minimum penalty.
There are rules for ranged pins, ranged sunders, and ranged feints, however; if One-Shot Bill was that sort of master with his bow, then he would probably have taken those feats as well.
There are other things he could do with his arrows as well to make them less lethal - fey craft, or using smaller arrows. There are also Arrows of Cure Light Wounds (whenever the arrow hits, it also heals).
Now, thrown weapons are a different thing altogether. Splash weapons are a ranged touch attack. Unless you are throwing something like a baseball at someone with the intent of really causing damage, tossing a coin or pebble at someone with the intent of it hitting their touch ac would indeed be a ranged touch attack.
Also, spitting on people is a ranged touch attack. The Eye of Gruumsh prestige class has Blinding Spittle, in which they literally spit in someone's eyes - and it's a ranged touch attack. The Spit Poison feat allows those that can deliver a poisonous bite to spit their poison instead - and it's a ranged touch attack.
PF vs. D&D 3.5e
The only difference between the two systems, regarding ranged pins and sunders and whatnot, would be CMB vs. CMD in Pathfinder which of course doesn't exist in D&D 3.5e.
Otherwise, the mechanics are the same. Touch attacks are touch attacks, and ranged touch attacks are ranged touch attacks.
Definitions
D&D Glossary: Touch Attack
An attack in which the attacker must connect with an opponent but does not need to penetrate armor. Touch attacks may be either melee or ranged.
PFSRD: Touch Attacks
Some attacks completely disregard armor, including shields and natural armor—the aggressor need only touch a foe for such an attack to take full effect. In these cases, the attacker makes a touch attack roll (either ranged or melee).
By the rules, only objects roughly the same size and weight as actual weapons your character can wield are allowed to be used as improvised weapons :
Improvised Weapons
Sometimes objects not crafted to be weapons nonetheless see use in
combat. Because such objects are not designed for this use, any
creature that uses an improvised weapon in combat is considered to be
nonproficient with it and takes a –4 penalty on attack rolls made with
that object. To determine the size category and appropriate damage for
an improvised weapon, compare its relative size and damage potential
to the weapon list to find a reasonable match. An improvised weapon
scores a threat on a natural roll of 20 and deals double damage on a
critical hit. An improvised thrown weapon has a range increment of 10
feet.
Thus an object too big to be a valid improvised weapon for your character cannot be thrown. Flavor text and the feats' names are sometimes misleading, what matters is what the rules clearly say and what is in the Benefit part of feats. Throw Anything uses "ranged improvised weapons" as key words, it's not valid for absolutely anything your character can lift.
Moreover, the Hurling rage power of barbarians would rapidly become useless if anyone strong enough could throw massive objects.
Best Answer
Only a tiny amount of official material even touches on improvised weapons. The feat Area Attack (Savage Species 30) is, quite simply, out of reach for most PCs. A creature that takes the feat Improvised Trip Attack (Dragon #295 73) can make trip attempts by hurling improvised weapons or actual weapons. The feat Improvised Weapon Proficiency (Dragon #295 73) doesn't actually grant it. The prestige class brawler (Dragon #295 72–3) should be awesome with improvised weapons—it does get proficiency with them at level 1—, but it's ultimately a letdown. And, short of taking a standard action to rub onto an improvised weapon oil of magic weapon [trans] (1st-level spell at caster level 1) (Dungeon Master's Guide 230) (50 gp; 0.1 lbs.) and similar substances—which may or may not work depending on the DM—, I don't know of any way to make an improvised weapon magical.
Officially, this is probably just too many hoops for too little benefit
One feat makes using improvised weapons better than using traditional weapons. The general feat Mercurial Strike (Dragon Compendium Volume 1 102) has as its benefit
Normally, it's impossible to realize this feat's benefit off-turn more than once per round: once a weapon's been drawn due to the feat's benefit, the wielder's no longer unarmed, and dropping a weapon is a free action, and that can't be done off-turn. However, an arrow—therefore a magic arrow—"that hits its target is destroyed; one that misses has a 50% chance of being destroyed or lost" (PH 113) no matter how that arrow is employed (see this question), and that includes an arrow employed as an improvised melee weapon.
C-c-c-combo! (definitely not broken)
The feat Mercurial Strike is the basis of the combination below. It's a mid-level trick for a mundane warrior. This is not a great trick, nor is it even a 100% reliable trick! However, it is a trick that works better when the trick's user employs improvised weapons, specifically ammunition that's destroyed on a hit and can be lost or destroyed on a miss.
Buy the DM pizza then ask the DM if a magic arrow's magical properties apply when a magic arrow is used as an improvised weapon. Mope if the DM still says No.
Get as much sneak attack damage or sudden strike damage as you can.
Take the following feats: Combat Expertise (Player's Handbook 92), Combat Reflexes (PH 92), Dodge (PH 93), Karmic Strike (Complete Warrior 102), the aforementioned Mercurial Strike, and Quick Draw (PH 98). (This can be done by a level 9 human ninja or rogue that has one flaw.) Plus, get a way to threaten your area while unarmed (see below).
As a class skill get the skill Iaijutsu Focus (Oriental Adventure 68–9). (Getting the skill as a class skill might take the feat acquired with a second flaw—I suggest the feat Academy Graduate (Savage Tide Player’s Guide 8).)
Get proficiency with improvised weapons. Several methods are listed here, but, in short, I recommend 1 level of barbarian with the alternative class feature city brawler (Dragon #349 92) then joining the affiliation Bloodbound of the Red Ring (City of Stormreach 99–102) and fighting arena battles until your affiliation score's 11. Those two combined mean you'll suffer no nonproficiency penalty with improvised weapons and you'll have earned the ridiculously metal title of—I kid you not—Slaughter Master! [Cue guitar solo.]
The alternative class feature city brawler also grants a barbarian the bonus feat Improved Unarmed Strike (PH 96-7), which means you now threaten an area while unarmed.
Wade into melee, trying to get hit using the feat Karmic Strike, and, in anticipation, maybe activating an amulet of tears (MIC 70) (2,300 gp; 0 lbs.), a talisman of undying fortitude (MIC 188) (8,000 gp; 0 lbs.), or the feat Stone Power (Tome of Battle 32–3).
When a foe does hit you, employ the benefits of the feats Karmic Strike and Mercurial Strike to make a melee attack with an arrow—or even, if it makes a difference, a magical arrow—against your flat-footed foe, dealing extra damage due to the skill Iaijutsu Focus and sneak attack or sudden strike.
The only melee weapon other than ammunition that I'm aware of that's destroyed on a successful attack is the ocanthus knife (Planar Handbook 77, 78) (450 gp; 1 lb.), which is, obviously, more expensive (and far heavier) than a mundane arrow but—more importantly—the knife does not, like an arrow, have coin-toss's chance of being destroyed or lost on a miss. In this regard, the arrow (or whatever kind of ammunition you prefer) is actually superior to the ocanthus knife: hit or miss, you want that weapon gone so you can make another attack if successfully attacked again, and there's at least a good chance of a dnd-3.5e fragile, elusive arrow disappearing even on a miss.
This trick is incredibly complicated, doesn't work all the time, and is kind of silly, but it's also sort of flavorful: imagine a human barbarian 1/ninja 9 who wades into battle with his bow, shooting arrows willy-nilly, hoping someone will make an attack of opportunity against him so that he can whip out an arrow and eviscerate that foolish foe that thought our hero unable to defend himself! That shtick plus ninja plus freakin' Bloodbound Slaughter Master of the Red Ring? [Cue guitar solo.] That's, like, right out of a 1990s indie comic. The grim-and-gritty adventures practically write themselves.
I know of no other way to make using an improvised weapon superior to using a traditional weapon. Further, I know that even this trick involves stabbing foes with rules-as-written autoannihilating arrows, which will rub some folks the wrong way. What can I say? I'm sorry, but I got nothin' else.
Licensed products' "secret weapons"
AEG's Way of the Open Hand (June 2004) is an officially licensed product bearing the Wizards of the Coast seal. I recommend the book only to those desiring entire runs of games as Hand's editing leaves much to be desired, but the text does include three feats that improve the value of improvised weapons:
The feat Himitsuheiki Novice (75) has easily met prerequisites, and the benefit removes the nonproficiency penalty for improvised weapons, grants a +1 bonus on attack rolls made with improvised weapons, allows improvised weapons to be treated as certain other weapons, and grants proficiency with the club, dagger, greatclub, spear, and whip. A not-horrible feat made more interesting by providing proficiency with both a martial weapon and an exotic weapon.
The feat Himitsuheiki Advanced (76) grants as its benefit, in addition to a bonus when making a feint attempt, the ability to succeed on an easy Spot skill check to take a move action to move up to 10 ft. and simultaneously acquire something that can be used as a weapon; further, if an unattended item can be used as a weapon (like, for instance, if it is a weapon) and it's within your reach at any time during your turn, you can take a free action to scoop it up (which is kind of cool if specializing in disarming, I guess).
The feat Himitsuheiki Master (76) doubles the wielder's threat range with improvised weapons (making the feat Improved Critical (improvised weapon) (PH 95) unnecessary, I guess, if the DM even lets that be a thing) and grants the creature once per round a +2 dodge bonus to AC when the feat's possessor intentionally drops a weapon.
The only other feat barely worth mentioning in licensed products is the don't-blame-me-I-didn't-name-it untyped feat Improvised Weapon Feat (Masque of the Red Death 117), the benefit of which allows the creature to take a move action to simultaneously travel up to 10 ft. and ready for use an improvised weapon extant in the environment… with which the creature automatically becomes proficient. However, Masque (Oct. 2004)—from Arthaus's Ravenloft line—is kind of a separate standalone game despite bearing the Wizards of the Coast-approved seal, so good luck with that. I mean, chances are you were probably already trying the DM's patience by looking through the regular licensed Ravenloft stuff.