Battle Moveset

A Good Moveset for Aggron would have to be this:

Attacks:

Earthquake
Focus Punch OR Iron Tail
Rock Slide
Hidden Power Bug OR Double-Edge

Items Attached:

Choice Band
Leftovers

Preferred Nature:

Jolly/Adamant/Impish

Strategy Using Aggron

This really is designed to be a Choice-Bander, but some people can't use those effectively and with a good attack stat it'll still do acceptable damage even without that 1.5 boost, although if you want to go non-CB you may want to get a Speed Boost (and preferably an Attack Boost) Baton Passed to Aggron.
Getting Aggron into the game isn't particularly hard, with such a huge number of resistances (it's a good switch into opposing Choice-Banders who will then be forced to make a switch, allowing you to get a free Focus Punch). If you know for a fact that a physical opponent has no super effective attacks it's a pretty safe bet that you can switch in with no problems (I.E Normal types with only Shadow Ball and Return).
HP Bug is for Celebi who will cause some problems for Aggron. Iron Tail is there for a filler over Focus Punch, in case you don't want to use it/can't use it effectively. Double-Edge isn't hugely great for a Choice-Bander since you want to get Super Effective hits, but if you can't get the right Hidden Power it's an acceptable replacement.
Rock Head is the preferred nature if you are going to use Double-Edge, but if not just go with Sturdy (1KOs are rare but it just means you have another move you can switch into freely).
If you aren't using the Choice Band, then go with Adamant, if you are using the Choice Band then go with Max Speed and Jolly (which will allow you to run out un-EV trained Pokémon of Base 90 Speed), however if your team needs a bit of defence then go with Impish.
Also, to those intending to baton Pass to Aggron, Max Speed and a neutral nature has a max of 199, which, with 2 Speed boosts will outrun Jolteon and his other (very fast) friends of Base speed 130.
(Also, for those intending to play Aggron on the OU circuit, you will probably want a Magneton on your team for getting Skarms and Forrys.)

EV Corner:

Max out Attack and Speed if you are using the Choice Band with this set.
Max out Attack and HP if you are using Leftovers.
Max out Attack and Speed if you intend to Baton Pass speed boosts to Aggron.

Strategy Against Aggron

There are two things that make Aggron a UU (I don't count that Surf weakness since it was never designed to take special hits anyway), a 4x weakness to Fighting type attacks and a 4x weakness to Ground type attacks.

- Strong Fighting and Ground attacks alongside strong Special Attacks (that are at least normally effective) are the way to take down Aggron, namely Earthquake, Cross Chop/Brick Break/Focus Punch and Surf.

- A nice Will-o-Wisp will nullify its only other good stat, its 110 Attack stat. You shouldn't be considering paralysing it since it isn't exactly the fastest Pokémon available (though if its got some speed behind it paralyse away).

- If your opponent has an Aggron on his team, and you can place a decent bet that it'll get switched in, predict the switch and use a Special, Ground or Fighting typed attack (or switch to a Pokémon with one). Nothing is more annoying (for your opponent) than switching in an Aggron only to have it get KOed in one move (which happens a lot with Aggron) before it even attacks.

Contest Moveset

A good Contest Moveset for Aggron would have to be this for the Tough Contest best with Impish, Lax, Relaxed or Bold Nature:

Attacks:

Harden
Take Down
Earthquake
Hyper Beam

Items Attached:

Yellow Scarf

Strategy Using Aggron

If you do the attacks in this following order you should have very few problems; 1st - Harden, 2nd - Take Down, 3rd - Harden, 4th - Take down, 5th - Hyper beam

Locations in Games

Ruby/Sapphire/Emerald Evolve Lairon Colosseum Trade from R/S/E Fire Red/Leaf Green Trade from R/S/E

Animé Appearences

Aggron has had an Animé Appearence. In it, Steven used it to get rid of Team Rocket from Granite Cave Episode 298: A Hole Lotta Trouble!