I am playing a 3.5 game with liberal inspiration from Pathfinder (we have Combat Maneuver Bonus/Defense, for example), and even heavier amounts of homebrew. Thanks to extremely high-powered homebrew classes, quest rewards, and worshiping the god of the healthy body, I can move 150 ft per round, or run 750 ft thanks to the Run feat, and essentially "flash step" another 900 feet on top of that (but everyone in this world can do that, so it's no big deal). I calculate this to be about 190 miles per hour, given six second rounds, and I'm interested in seeing if I can break the sound barrier (about 750 miles per hour).
What magic items or feats are available to a character in either 3.5 or Pathfinder to boost their speed? I already have haste and expeditious retreat on me thanks to perks from worshipping the right gods and from permanent runes I received as a quest reward, and I already have the Run feat. I also want to achieve this speed by myself, so no outside assistance by cohorts or PC spellcasters. I am an 11th level gestalt between a Swordsage and a homebrew class called a Tenken. I'm planning on taking Master of 9 for the swordsage soon. Currently, I can take an extra turn 1/encounter with the Tenken, and at 20th I get the extra turn every round, so I don't want to sacrifice anything to multiclassing. I am a homebrew race called the Aericetus, which has
+6 dex, +6 Int, -2 str, -2 con, Swim Speed, Darkvision 300ft, Sneak Attack+1d6, Spellfire: Absorb spell energy directed at you and return fire
Best Answer
I am largely uninterested in how similar results can be achieved in Pathfinder, so I've narrowed this to Dungeons and Dragons 3.5. I am also uninterested in changing forms, but I assume doing so adds significantly to these totals; I'll leave that exercise to another. This was exercise enough. Undoubtedly, there are bits and pieces here and there that can add to these totals, and already using haste, expeditious retreat, and the homebrew class are significant.
Dungeons and Dragons 3.5 feats that increase land speed
There are a lot. Like Sturgeon's Law says, most of them are terrible. Note that some of these feats were originally printed prior to the Dungeons and Dragons 3.5 revision and may be subject to minor adjustments by the DM (DMG 4). I'm pretty sure none grant enhancement bonuses so they should all be usable while the expeditious retreat spell's duration continues. The following list is alphabetical.
It's probably too difficult at this point to get the feats Cheetah Tribe Sprint (ShS 19), Divine Alacrity (Faiths of Eberron 145-6), Divine Vigor (Red Hand of Doom 126), Fire Feet (Dragon #311 40), Fury’s Focus (Dragon #304 84), Imbued Healing (CC 60) to use it with the domain Travel, Improved Power (Travel) (Dragon #342 21), Initiate of Fharlanghn (Dragon #342 51), Longstride Elite (Races of Eberron 114), Mark of Malbolge (Fiendish Codex II 84), Minor Shapeshift (Complete Mage 45), Prophecy’s Explorer (Magic of Eberron 50), Rage of the Raptor (Dragon #315 26), Speed of Thought (Psionics Handbook 29), Swiftness of Orien (Player's Guide to Eberron 48), Technomagic Implant (Dragon #351 93) for the cheetah's swiftness implant, and the trait Quick (Unearthed Arcana 89).
Unless shenanigans are used, Epic Speed (Epic Level Handbook 54) is likely unavailable, and it'll requires some serious persuasion to allow the psionic feat Psionic Boost (Expanding Your Mind Web column “New Talents, Feats, and More”).
Finally, it's probably too late to pick up the regional feat Fleet of Foot (Player's Guide to Faerûn 38), the dragon-only feat Improved Speed (Dr 71), or to be a saurian shifter with the shifter trait junglerunner (Dragon #328 63).
Dungeons and Dragons 3.5 magic items that increase land speed
I'm pretty sure none grant enhancement bonuses so they should all be usable while the expeditious retreat spell's duration continues. This list is also alphabetical.
It's a little difficult to find a magic item enabling consistent use of a personal spell by a non-caster, especially seeing as how the skill Use Magic Device isn't a class skill for the swordsage or the tenken. Assuming the creature's not devoting cross-class ranks to the skill Use Magic Device, a handful of mildly distasteful options remain: the feat Attune Gem (Magic of Faerûn 21) creates at potion prices plus 50 gp per spell level gems that the user can crush as a standard action to cast such spells, and the feat Craft Wondrous Item allows the creation at potion prices spellworms (Dragon #343 80-1), an internal spell storing parasite that allows a spell to be used either as a standard action like a spell-like ability or as a full-round action like a spell (the text is contradictory). More palatable—and pricey—is something like a ring of spell storing, but this might involve more than is comfortable a friendly caster. Below I've assumed spellworms (and a standard action) because they're hilariously gross.
The belt of battle (Magic Item Compendium 73) (12,000 gp; 0 lbs.), in addition to granting the wearer a +2 competence bonus on initiative checks, allows the wearer to take a swift action to spend 1, 2, or 3 charges to gain a move, standard, or full-round action, respectively.
Undoubtedly other sources of speed increases can dug up, but these are what I knew of off-hand. It's likely enough, but Dumpster-diving for even more is certainly a option.
"How fast is that?"
Using just the resources in this answer—excluding bonuses from expeditious retreat, haste, and the homebrew base class, for instance—, consistently, this isn't as fast as you want, but, in a burst that expends a lot of resources for only 1 round, it's way faster than you need.
Turn 3: Activate the feat Sprinter to gain for 1 turn a +10 ft. bonus to speed; this is not an action. Discharge the effect of the spell footsteps of the divine to gain for 1 round a +390 ft. bonus to speed (assuming an actual not relative duration); this is not an action. Take a full-round action to run. That's a speed of 515 ft. that's doubled via the magic weapon rapid wrath that's ×5 via the feat Run to 5,150 ft.
Take a swift action to activate the belt of battle to gain an additional full-round action and take another full-round action to run. That's another 5,150 ft.
Your turn should be over, but take an immediate action (spending the next turn's swift action) to activate the spellworm of greater celerity to take a third full-round action. On this full-round action, charge a foe, object, or square at ten times your speed via the feat Cheetah's Speed. That's another 10,300 ft. that's ×2 due to the maximum distance a creature can charge during a round.
This round, you've traveled 30,900 ft. in 6 seconds. That's about 3,500 mph, or over mach 4.5, which isn't even close to the speed of light but should be sufficient.
I don't want to get into Internet scuffles with anyone, so if it rubs you wrong to have activated the spellworm of greater celerity this way, skip that step and subtract 5,150 ft. from the total for, instead, about 2,900 mph or about a generous mach 4.
Note that Dungeons and Dragons 3.5 uses real-world multiplying for real-world things like speed (PH 304); this is slightly different in Pathfinder but not much, but, as always, ask the DM.