Primeape

Type Tier
Fighting UU
Statistics
Stat
HP
65
333
Atk
105
308
Def
60
218
Spc
60
218
Spe
95
288
Name Moveset

Physical sweeper

~ Submission
~ Rock Slide
~ Body Slam
~ Focus Energy / Hyper Beam

If you're playing on Stadium, just Focus Energy and blow them away with a slew of Submissions, Rock Slides, and Body Slams (or Hyper Beam if you prefer). If not, replace it with Hyper Beam, since Focus Energy only works in Stadium.

Other Options

If you don't like Submission because of its recoil, try Low Kick. It's weaker, but has less of that nasty aftertaste, and can flinch too. With Focus Energy and a little luck, Thunderbolt/Thunder will do some quite damage to Water-types, especially Starmie. Dig is cool against Muk, Nidoking, or Nidoqueen. Remember that while it has 100 Base Power, Dig is easily countered.

Opinion

Primeape is in his prime in UU. He can wreak havoc against the UU metagame, even if he is a little on the fragile side. He's a sweeper, and a darn good one for UU.

Counters

Primeape's defenses are weak, so most opponents that resist Fighting and won't die immediately to the other moves will do. For instance, Psychic-types (especially Slowbro and Exeggutor) and Gengar are completely impenetrable to Primeape, as are Poison types like Muk and Weezing. Flying Pokemon that aren't 4x weak to Rock Slide and have Flying-type moves, such as Zapdos in OU and Fearow in UU, also work.