I'm wanting to know what champions reward being aggressive, and are actually built for that (Don't die if you look at them wrong; have the ability to survive; etc.).

Any champion can be played aggressively, you just have to be careful when you do it. It all depends on your lane match-up. For example vayne can't really be aggressive against graves, not early anyway. On the otherhand, graves HAS to be aggressive against vayne, or she will completely outscale him lategame and just wreck.

any tank

Have you tried Kog'maw? Enjoyable to play, Just requires a little support.

Renekton and Riven are probably some of the most aggressive champions early for top lane. LeBlanc Is amazing for that mid lane. Miss Fortune and Graves are probably the most offensive ADC's early. Blitzcrank, Alistar, Taric, and Leona are the most offensive supports.

I kinda figured Graves would be one of the champions listed because I main him as an ADC, and I notice that I win a lot with him because he rewards the aggressive play style and his passive is built for it.

Top lane, Irelia, Jayce, are safe aggressive picks. If you just want to have fun you could play assassins like Akali who are obviously extremely aggressive but at higher levels of play can be hard to use properly if other team has oracles, a lot of cc to keep you in place when you dive on them, or smart and just focus you down first.

As for Mid lane I would recommend people who have good wave clear and strong roam potential, such as Ahri or Gragas. Both have amazing mobility to quickly gank lanes and are fun to play.

Junglers, I would recommend gank heavy junglers like Maokai, Lee sin, Skarner to some extent

As for AD carries, there is minor aggression you can do outside of your lane phase due to AD carries being the weakest champions without items, but late game you will have a lot of fun. For a aggressive bot lane, go Leona, Blitz, Taric, Sona with the standard AD's Corki, Graves, Ezreal

Blitzcrank...

he's all aggression. you literally just push people around, zone, bully all game.

In lane you force people away from their cs, and if they don't you make them fight, out tank them, and if they run you pull, pop up etc. etc.

literally all game you play blitz as the powerhouse initiator. I often find when playing him, my team literally falls in behind me, and fights don't happen unless blitz makes them happen. He wins by capitalizing off of enemies' mistakes, he's tanky enough to stay in the fight, he's got enough utility to change team fights in so many ways.

You want aggression...play support blitz with an adc...you start out kinda slow and calculating, but by the end of the game you are 200% at all times.

Soraka, go kill people with e-q combo

If I have to pick one champion at random, I think sion makes a good aggressor. His R heals you and your allies based on your autoattack damage so you have to hit hard and fast in order to heal fast enough to survive. Would be interesting to see him on a team with a soraka who has a heal summoner spell, so much sustain...