Superman - Keanu Reeves. This Superman would be young in his career and earnest, yet supremely likeable and commands strength and respect by presence alone. I'd play up the alien aspect.
Batman - Ralph Fiennes. A hardened Batman possibly 10 years into activity. Someone who could be both a mentor to Reeve's Superman but also at odds with each other. Fiennes as the sophistication and cold eyes to play socialite Bruce, and the fury and intelligence to place a Batman truly to be scared of.
Wonder Woman - Gillian Anderson. Bridges the gap between Reeve's Superman and Fiennes Batman. She is the de facto leader of the league, capable of agreeing with Clarke or Bruce depending on the situation.
Green Lantern - Brad Pitt
Flash - Woody Harrelson. The potential these two would have as a duo would be too hard to pass up.
Aquaman - Benicio Del Toro. Foreign and supremely protective of his people, comes to the surface begrudgingly and is helped into coming together with the League by Freeman's Martial Manhunter.
Martian Manhunter - Morgan Freeman. The father figure to the league. A regal alien who has possibly more compassion for humanity than the rest of humanity has for itself. Understands the bigger picture in terms of the threats out there.
Lex Luthor - Tom Cruise. On the outside a popular figure who has used Lexcorp to better the lives of Metropolis, but secretly a narcissistic maniac who is using the less fortunate in Metropolis as guinea pigs in his experiments to try and crack the "meta" gene. Absolutely hates Reeve's Superman with a passion like no other. Just to note this isn't an attack on Cruise, I just think he'd be an amazing Lex.
Darkseid - sorry, have to tap out on this one and enlist the talents of Andy Serkis. I don't think this voice should be in any way recognisable or even human sounding, so I wouldn't use an famous actors. His voice would have be gravelly and alien, yet with a hint of sneering regality. Serkis would be the man for this.
I'll try to think of more but happy to take any comments as I get some of the above would be controversial.