My response deals only with D&D. Although I own, have read, and have evn played a few other D20 games, none have really caught on in my group. We're pretty much D&D-exclusive.
My biggest pet peeve is the fact that at a certain point what a character owns becomes more important than what the character himself can do. In other words, I'm against the proliferation of magic item "trinkets." (For example, if a character, by level, should have around 16,000 gp worth of magic items, I would vastly rather see the character with two 8,000 gp items than with eight 2,000 gp items. In D&D, the latter is what occurs, and is, in fact, what the game is designed for.) This has been a problem throughout the history of D&D, but it's a very difficult thing to eradicate in 3E because so many rules subsystems are designed to interlock. Messing with magic items throws challenges off, which throws advancement off which ...
Lesser peeves?
The high variability of hit points. A character's hit point total is arguably his or her single most important stat. Leaving such a vital rule vulnerable to so much variation is just ... silly.
Designing the game for a square grid, rather than taking the redesign as a chance to move to hexes. Yes, drawing maps on hexes is slightly more difficult than drawing maps on squares, but only to the extent what is drawn fits the grid in the first place. Also, once the map is drawn, every other aspect of play becomes simpler and more consistent.
Random stat generation. I have never yet encountered a player who prefered to randomly roll stats, though many claim such a preference. These are, instead, actually players who prefer the chance of rolling really well, coupled with the chance to whine and (in extremis) commit PC-suicide if stuck with mediocre or below average stats. I'll never again allow my players to randomly generate stats.