In the last year I've run or played:
Spirit of the Century
Based on FATE 2.0, which evolved from FUDGE. Probably my favorite system overall, the key to the system is Aspects, which are player-designed character traits that power the Fate Point economy. It's a pulp system (1920s high action, ala Indiana Jones), but related games cover hard SF (don't know the name offhand; it's recent) and space opera (Starblazer Adventures), and the Dresden Files RPG (based on Jim Butcher's urban fantasy novels) is coming soon... or at least soon-ish.
Initiative is handled via Skills:
In a physical conflict, the character with the highest Alertness goes first.
In a mental or social conflict, the character with the highest Empathy goes first.
Resolve is the tiebreaker, and if that's also tied the player on the GM's right goes first.
You can also ignore initiative and go clockwise around the table; that's a provided variant rule.
Mutants and Masterminds 2e
A supers system based (very loosely) on the d20 system. It's a one-die system (only the d20 is ever used), character creation is done via point buy (like HERO only much simpler), and powers are extremely flexible due to the ability to substitute any power that's appropriate to the character's power source for a very low cost.
Initiative is handled via rolling d20 + Initiative bonus, ala standard d20, but being a supers system, you can get *extremely* high initiative scores.
Champions
A supers game using HERO System 5th Edition. A lot like Mutants and Masterminds, except slower, more complex and less flexible.
A system I liked a lot more before playing M&M, which does basically the same thing but better in almost every respect.
Ironically, the sole area in which I still prefer HERO to M&M is, in fact, Initiative!
In HERO, characters have a Speed stat (normally ranging from 1-12) and a Dexterity stat (unlimited, but approximately 5-20 for adult normal humans). A character acts a number of times per turn equal to his Speed, so Speed 6 allows you to act on phases 2, 4, 6, 8, 10 and 12, while a Speed of 4 allows you to act on phases 3, 6, 9 and 12. When two or more characters act in the same phase, they go in Dex order.
Dungeons & Dragons 4e
A fantasy tactics-RPG using an advanced form of the d20 system, with the most popular brand in roleplaying. It focuses on teamwork and tactics in a high fantasy environment. Wait, you knew about this one?
Anyway, I don't think I have to explain D&D 4e initiative, and it's the same as M&M anyway.
Star Wars Saga Edition
Another d20-derivative, an no, I'm not describing freaking Star Wars.
In my view the best example of the original d20 branch, but it's hard to go back to now and I haven't run it since using 4e.
Initiative is d20 Initiative, same as always.
Call of Cthulhu
I... honestly, despite playing this recently, I don't remember how Initiative works. We didn't do a lot of fighting and I don't own the rulebook.
I recall it working somewhat like other BRP games, though:
Guns go first, then weapons, then unarmed (including monsters, the only reason it's possible to survive a fight with many of them). Ties are resolved by Dex. Then, characters who can take extra combat actions (due to high Dex) take their remaining actions after all three types have resolved, in the same order.