Possible official solutions
Most of these require being prepared for this situation and have the appropriate class/feat/skill trick/magic item, but they work. The ones that don’t require any of those things... maybe work, maybe.
Epic Tumble
Per the Epic Level Handbook, standing from prone as a free action is possible with a DC 35 Tumble check. According to the core rules,
Free actions rarely incur attacks of opportunity.
RAW, nothing in core/SRD says that standing from prone as a free action with the appropriate Tumble check causes standing to no longer provoke, but it would seem appropriate, and bear in mind that Epic Level Handbook was written for 3e and only “updated” later, and in 3e standing didn’t provoke.
However, Rules Compendium also covers this rule on page 94, and explicitly says
Standing in this way still provokes attacks of opportunity.
Get to your knees first, then stand
The core combat modifier rules mention kneeling, which has half the penalties of being prone. There is no listed action for moving from prone to kneeling, or from kneeling to standing, but many feel comfortable assuming they’re each probably move actions. Since there’s no listed action for them, there’s nothing that says they provoke—so some have argued they don’t.
In this way, you can stand by taking two move actions (your full turn outside of swift or free actions) without provoking. But it requires enormous amounts of squinting to pretend this is an official rule. People do it, but they’re really projecting; it’s a reasonable enough ruling but the rules really don’t endorse it.
Personally, my read of the situation is that kneeling is a type of standing, and you can kneel or stand from kneeling as a free action, without provoking, but moving from prone to kneeling is the same as moving from prone to standing and requires the same action and provokes the same attack. I don’t know that this is a good ruling (it’s never come up in my games), but it seems like a more honest reading of the rules.
Buy a pair of boots of agile leaping
The boots of agile leaping from Magic Item Compendium allow you to stand from prone as a swift action that doesn’t provoke if you have 5 ranks in Balance. Simple, and they’re really cheap, so... I guess everybody should just buy them? Everyone should already prioritize 5 ranks in Balance, since you need that to avoid being flat-footed any time you’re balancing.
Get skilled and get tricky
There are two different skill tricks that enable standing without provoking, Nimble Stand and Back on Your Feet (which also enables the standing as an immediate action). Nimble Stand requires 8 ranks in Tumble while Back on Your Feet requires 12, so that’s a minimum of 5th and 9th level, respectively, which is a bit rough. More importantly, skill tricks are only usable once per encounter.
There’s a stand spell
The spell stand from Player’s Handbook II is a 1st-level spell that stands the target up from prone as an immediate action without provoking. Immediate-action spells don’t provoke, either, so this is effective if, ya know, you have 1st-level spells from an appropriate list (sor/wiz or duskblade, officially).
Thief-acrobats get kip up
A 1st-level thief-acrobat (Complete Adventurer) gets “kip up,” which is a free-action stand from prone that explicitly doesn’t provoke. Requirements are mostly trivial (no feats, quite a few skill ranks but in good skills), but you do need to have evasion which can be a bit of a pain.
Important context:
All that said, on the broader issue of trip and other maneuvers...
Attacks of opportunity resolve before the provoking action
...so you cannot trip someone who is standing from prone, because when you make the attack, they already are prone. Since you can’t trip them, you do not get the extra attack from Improved Trip.
That means that, with Improved Trip, you get to trip with a follow-up attack, and then attack of opportunity again when they stand, but then after that they are standing and can now act normally. They have to do something that provokes another attack of opportunity for the tripper to have a chance to knock them down again.
Trip is strong, ish. Other maneuvers are just awful.
Trip is pretty strong. It’s got nothing on even low-level spells, but still, pretty decent maneuver. And for that reason, you see it completely overshadowing every other maneuver.
Because every other maneuver is not “pretty decent.” They’re outright terrible.
So looking to nerf trip is a poor choice, because trip is the one maneuver actually worth using, the one “Improved X” worth having.
Bull rush is great for dungeoncrashers (Dungeonscape), but otherwise extremely situational. Still, Improved Bull Rush is a great feat because it’s required for Shock Trooper. A shock trooper will never waste a turn on bull rush rather than a pouncing charge, but still.
Disarm is useless against a huge variety of foes, and against those it is useful against, an 8-gp mundane item gives them a +10 bonus, which means you may as well not even bother.
Feint eliminates your chance to attack, and Improved Feint still eliminates your chance to full-attack. There is no reason—ever—to agree to those terms. A martial character needs to full-attack every turn. Especially one that cares about foes being flat-footed, since that is probably a rogue and therefore needs full-attack to actually use both of their weapons.
Beguilers (Player’s Handbook II) and invisible blades (Complete Warrior) can get the ability to feint as a swift or free action (respectively), which could be good, but beguiler requires 6 levels in a spellcasting class without sneak attack, and you still have to take Improved Feint, and invisible blade requires 5 levels in a prestige class with brutal requirements.
Grapple is monstrously complicated, and at-best locks one foe down. It’s extremely difficult to do as a PC, since it relies so heavily on size. This one is better than the rest, though, because if you jump through the appropriate hoops, you can lock down one foe really well, and sometimes that’s a really big deal.
Of course, the best “grapplers” are summoners, since they can lock down multiple foes, and also leave themselves free to do other things. Grappling is really strong for summoners, but they won’t be taking Improved Grapple, they’ll just summon things that have.
The only point of overrun is to try to charge someone behind an enemy. That means Improved Overrun is worthless, as now you have no chance of going through that enemy and guarantee you’ll be blocked. Without Improved Overrun, it’s up to them, but at least there’s a chance.
Sunder destroys your own loot, and most weapons worth sundering are way, way harder to destroy than the people carrying them. And again, same problem as disarm where a ton of foes don’t have weapons in the first place. Has niche use against a hydra, but unless you’re a dedicated hydra-killer, that isn’t worth a feat.
So even if Improved Trip didn’t exist, no one would use these. They’d just use charging or something else instead. None of them is worth using, and not because trip exists, but because they just aren’t worth using. Maybe grapple, particularly if you count grappling done by summoned monsters. But for the rest, the only people who ever use either are those who don’t understand their flaws, or those doing it as a self-imposed challenge.
Nerfing trip doesn’t solve any problems, it just adds another maneuver not worth using. For example, see Pathfinder, where they did nerf trip quite severely, and buffed e.g. sunder, and yet grapple and trip (and some new PF maneuvers like dirty trick) are still the only maneuvers worth using. That’s because fundamentally, trip is still a decent thing to do to an enemy (even if PF makes it cost so much more), while the others aren’t.
