Let's see, champions I play often...
Fiora would get Frozen Mallet. She has issues sticking on people and this would allow it. In a 1 item meta her innate damage from w and IAS from e would just have to gover the gaps, plus survivability is always good.
Trundle would get Trinity Force. He has the ability to stick already, the built in Sheen prock works well with rabid bit, and it's an all around great item.
Hecarim would get Ghost Blade. Assuming most people would't grab boots it would be fine not to have them myself. The activated ability gives the killing power or escape power you need.
Rammus: Thornmail. 'nuf said.
Veigar's Q is all the AP you need... or is it? Rabadon's so you could just melt the opposition.
Kassadin needs his mana and AP, so Archangel's Staff.
Ryze would get Frozen Heart, be the team's tank, and still get sweet sweet damage out of it.
I don't ADC, like, ever...
Doesn't matter who, Taric, Soraka, Sona, Leona, Lulu... WARDS. Wards, wards, wards. Wards.