Suggestions for Passive Scaling Champions?

Hello! I'm a deep fan of League of Legends, and I've been playing for several months. I had made a request on the forums a few months ago about what champions can best be played aggressively and do extremely well. Now I'd like to ask the inverse question: Which champions can be played passively and scale incredibly hard into late-game? I know about (who is my favorite champion thus far) but lately I've been finding that my attempts to play aggressively are met in kind and I end up losing more than half of my trades (usually due to 1 second on my Q or 2 on my E, but I digress)

Which Champions, preferably Mage, can neglect trading and focus purely on farming, and then be an absolute monster in end-game? My early-game isn't that great, and my mid-game is acceptable, but usually it's end-game that I can really establish dominance in team fights and overall.