Three champs spring to mind as being both kings of early game harassment and late-game domination - Tristana, Fiddlesticks and Nunu.
Tristana is one of the most frustrating opponents imaginable if played to her strengths as a solo mid. I've played her a lot, and with the exception of a well played Yi (Alpha strike is a pain in the arse) and Fiddlesticks (Drain... ugh), I've yet to face a champ that I can't completely dominate, some to the point where they can't even get in range to last hit. She's an excellent farmer thanks to explosive shot, rocket jump gives her both chase and an panic button, and the explosive shot active is very powerful early game, particularly against other squishies. Add in her range, and she's a very dangerous foe early on. Late game, thanks to rapid fire, she can reach insane amounts of damage.
Fiddlesticks is a real terror, as casters go - Terrify is a surprisingly frustrating disable, Dark Wind is a nice farming tool and harassing spell, and Drain gives him a huge amount of sustainability. Late game, he retains all that, and also has Crowstorm, which can quickly change the dynamic of a team fight. His abilities also start out pretty cheap mana-wise, so they're reasonably spammable.
Finally, Nunu is a fairly devastating force if allowed to get going. I wouldn't try to solo mid with him (got my doubts about melees being there), but Ice Blast does huge damage and slows, while Consume regens a massive chunk of health. Blood Boil, combined with some good boots, can make him virtually uncatchable if it comes to a chase. I've gone 1v2 with Nunu and not only held my tower, but even got kills just through Ice Blast. And then there's his ult... the channelling time is a weakness, yes. But it's an AoE effect that slows and can, with the recent BUFF, easily do 2k damage. Oh, and he's got enough health that, with the right items, he can be a half-decent tank.