Muk loses to many common Pokemon in standard play. This is not because of its stats or movepool, but thanks to its weakness to the most-used physical attack in the game: Earthquake. Overall, you won't find Muk doing much except surprising opponents and of course Exploding.
Thanks to its low Speed, high HP, and great Attack, Muk is a fantastic user of the SubPunch strategy. Fire Blast hurts common Steel-type switch-ins, such as Metagross and Skarmory, while Hidden Power Ghost makes it one of the best Gengar counters in the game.
The HP investment lets Muk make 101 HP Substitutes, and the Attack investment and choice of nature increase its power output. Muk needs a Special Attack stat of 182 to 2HKO Skarmory with Fire Blast or Thunder; a stat of 197 is needed if using their less powerful alternatives, Flame thrower orThunderbolt. Be sure to use a Speed-lowering nature instead of a Special Attack-hindering one if running one of these special moves.
With great Special Defense and Attack, like Snorlax, Muk makes a decent Curse user. A Curse-boosted Explosion is powerful, but Rest lets it keep on tanking. Watch out for Psychic and Earthquake, however.
Aside from Attack, this set should focus on Special Defense as Curse will make it bulkier on the physical side. Again, 182 Special Attack is needed to 2HKO Skarmory with Fire Blast or Thunder, and 197 to do so with Flamethrower or Thunderbolt.
This has the potential to be effective, but is more of a novelty than anything. Prediction is required to use it well; other than that, it can switch in on the same attacks. Brick Break is an option to OHKO Tyranitar without having to resort to Focus Punch.
Body Slam can paralyze the opponent, which is always handy. Imprison is unorthodox and might work in rare circumstances, but it is recommended that you stay away from it until you've tried out more standard variants. Memento can make your opponent's Pokemon harmless and set up a sweep for a Belly Drum user; Explosion is more recommended for suicide, though. Flamethrower and Thunderbolt are alternative options to hurt Skarmory, but their more powerful variants are generally superior. Rest—with or without Sleep Talk—extends Muk's lifespan; however, it provides Muk's counters with an easy switch-in.
Checks and Counters
Steel-types, particularly Jirachi, Skarmory, and Metagross, are immune to Sludge Bomb. They tend to take quite some damage from either Focus Punch or Fire Blast, but with Earthquake, or in Jirachi's case, Psychic, most of them should be able to best Muk one-on-one.
Ground-types such as Claydol, Rhydon, Swampert, Donphan, and Golem can pick Muk off with STAB Earthquake; furthermore, they resist Sludge Bomb and pack enough Defense to shrug off most of Muk's other attacks. Focus Punch might hurt Rhydon and Golem, though, and the rarely-seen Giga Drain or Hidden Power Grass can shut them down for good.
As for Rock-types, Regirock also packs Earthquake while resisting Sludge Bomb and Explosion, and has such high Defense that it doesn't much care about Focus Punch. While Tyranitar can't take Fighting attacks, it resists Sludge Bomb and Fire moves, and often packs Earthquake.
Suicune can take most of Muk's physical assaults, Roar away Curse boosts, Calm Mind up, then Surf Muk into oblivion. Gengar 4x resists Sludge Bomb and is immune to Explosion and any Fighting or Ground moves Muk might be packing, so unless Muk carries Hidden Power Ghost or a move such as Thunderbolt or Fire Blast, Gengar will beat it one-on-one, especially if Gengar carries Psychic. Weezing can cripple Muk with Will-O-Wisp unless it puts up a Substitute in time.