You're looking at DPS, not Damage, right?
Two Handers tend to be slower - you attack much less frequently - but hit much harder. This is particularly useful in combination with the way several channelled or high-cost skills work - you'll conserve your resources more while doing comparable damage with a big heavy weapon, at the cost of defense, or possibly some extra damage. You'll also want to take a look at this question for a rundown on dual wield mechanics:
How is listed DPS calculated when dual-wielding weapons?
(Your class also comes in to play here. For example, Demon Hunters using a 2h such as a Bow instead of a Hand Crossbow can still equip a Quiver in the OH, retaining the stat bonuses from the offhand slot).
In general, I completely ignore whites and grays - typically they're worth less than 10 gold a piece, which is not even worth dragging back to town. Do note that some "special" objects such as health potions and gems have white text, which might be confusing if you're completely ignoring that font color categorically.
In the very early going, when you have equipment slots that are completely empty, they're worth grabbing just so you're not completely naked. In particular, when you're just starting out, keep an eye out for a Targe shield - it's got typically around 50 defense, which outclasses most of the defense you'll find on any other item at this stage of the game.
In the very early phase of the game, you can occasionally find a white weapon/armor piece that has slightly better DPS than your current weapon - I've found white weapons better than blues I had from previous dungeons in the early levels previously. For this reason, sometimes I'll grab (or do a quick check by hovering over it and pressing CTRL, as bwarner notes) the first white item of a type I find, just to see if it's a class better than my current gear.
Past about level 5 or so, though, you're better off leaving them where they drop. Once you have items that give you beneficial stat boosts beyond the basic defense/DPS rating of the item, whites and grays are almost always going to be worthless to you. Even if you can get a few extra DPS or defense points out of a "higher tier" white, it probably won't offset the utility of the other bonuses on your current gear.
Best Answer
Strength increases your Armor by 1 point per point.
Dexterity increases your dodge chance by 0.01%-0.1% per point.
Intelligence increases all resistances by .1 per point.
This has a number of interesting effects - most notably, because of the way Resistance works (it's functionally identical to Armor), stacking small amounts of Int on a Barbarian, Demon Hunter, or Monk can result in a dramatic survivability increase.
Resistance, like Armor, will reduce all damage you take, and, like armor, you gain substantially larger marginal benefit by increasing it when you don't have much. Since typically, a Monk (for example), will have a reasonably high Armor stat from gear and passives, and very low Int, adding just a little bit of Int via an oddly itemized piece of gear can provide a really large survivability boost - certainly more of one than trying to add Armor via Strength.
However, because everyone has a decent amount of Armor inherent in their items, increasing Strength for a similar benefit is generally not worthwhile unless you're playing a Barbarian that wants the damage boost as well, or a Wizard or Witch Doctor with a very high Resistance stat already.