My list:
Lara Croft (Tomb Raider): action, history, technology and some occultism. It's like Indiana Jones, but sexier, and every LoEG must have a girl.
Dr. Gordon Freeman (Half Life):this guy has a PhD in Physics from MIT, fought with hordes of aliens, without backup... with a Crowbar. He was voted the "All Time Greatest Video Game Hero" in 2008.
James Bond (007) or Ethan Hunt (Mission: Impossible): the "super-agent" is an iconic image, so one of them could not be left out.
Bruce Wayne (Batman Begins) or Antony Stark (Iron Man): power through technology, heroism and fancy wardrobes. Both are rather old characters, but their newer versions blend very well with the 2000s.
Hellboy: again, occultism, science and action usually results in LoEG. Plus, the team needs a Bruteforce guy.
And one of those, as we don't want a league with 300 members:
Robert Langdon (Da Vinci Code etc): some occultism, some science and much more action than you would expect from a professor a Symbology Professor - he deserves a place as much as Sherlock Holmes deserved in the classic League, even if he never entered it.
Jack Bauer (24): he overlaps with the super-agents, but is more 2010'ish.
Jill Valentine(Resident Evil): I don't remember any league with more than one woman, but...
Dr. Gregory House: he doesn't really fit with the whole idea, but... gah, he deserves it.
Others that could belong to the League, but would sound too off/controversial, are:
-Spiderman: we don't need another superhero
-Harry Potter and Potterverse in general: difficult to blend with the rest of the group, and would sound rather silly.
- Agent K or J, from MiB: they're nothing without MiB, and the League is always formed by extraordinary people, not organizations.
-Indiana Jones: wrong decade, but Indiana Jones deserves his own League - he and James Bond in the same organization... that would be epic. His son, though, wouldn't be that bad.
-Characters from 1984 or V: wrong decade, again.
-Neo or other from Matrixverse: too hard to fit in.