Plan your lanes. Regardless of how good a lineup is lategame, if they can't synergise properly in the laning stage, you won't get to the lategame. For example, a lane of two tanks against anyone even slightly good at harassing will be murdered.
Always try to have at least one ranged in each lane - some melees can sub in due to abilities (Nunu with iceblast spam and consume, Yi due to alpha strike, Kayle due to temporary ranged ability), but in general you'll just get harassed too badly with no real counter.
After that, consider your CC. Morgana and Ryze in the same lane will be hell to escape from with two snares, but maybe just one combined with some DPS would be better? Frees up the other to help out in another lane, and doesn't rely so much on mana-hungry burst. Don't forget that anyone can take Exhaust for CC.
Get a decent split of magic and damage. Anything else runs into the problem of easy MR/armour stacking, and runs into other issues; a caster heavy team will do horrible things in a team battle, but if you don't wipe them out instantly, you're in for a lot of pain while your CDs go down. A full DPS team risks losing people to nukes without being able to respond in kind.
The team I run alongside a lot varies a bit, but Twitch/Yi/Nunu/Tristana/Eve isn't unusual. Two slows (I don't count rocket jump), a stun, a nice blend of casters and damage, and a couple of assassins to make the enemy jumpy. Main weakness is lack of a true tank, but Nunu can sub in if well supported.