Battle Moveset

A Good Moveset for Blissey would have to be this:

Attacks:

Softboiled
Heal Bell
Toxic
Counter OR Seismic Toss

Items Attached:

Leftovers

Preferred Nature:

Impish

Strategy Using Blissey

Alot can be said about Blissey, its HP is the highest in the game and its special defense is well above average. To attack Blissey with special attacks is rather stupid.
Blissey also learns a few moves that allows it to recover HP and cure status conditions. For its ability, I would pick Natural cure, just in case Blissey is subjected to the sleep status condition.
I find that Heal bell is quite effective, you'll understand why if you use Toxic against a Pokemon with the Synchronise ability, this way you can Toxic your opponent without worrying about being poisoned due to Synchronize.
Softboiled is a must due to Blissey having a really high HP, and since Softboiled recovers 50% of maximum HP, it will come in handy.
Since Blissey is more likely to be attacked by Physical attacks, Counter could possibly be included on this moveset, so if you're opponent fails to knock out Blissey with a Physical attack, the damage it deals back should be high.
Another possibility to replace Counter with is Seismic toss, I've found this move provides some use if you're up against a Pokemon with high defense (Seismic toss will do 100 damage to your opponent's HP, if your Pokemon is level 100).
Its no surprise that Blissey is frowned upon with those stats, and most people tend to leave Blissey well alone when it comes to battling, since many people might consider this pokemon 00ber and have an unfair advantage over your opponent.

EV Corner:

Max out the EVs in Defense & Special Defense for Blissey with any remaining in HP

Strategy Against Blissey

Blissey has incredibly high Special Defense but it's Physical Defense is incredibly low so any Physical Volley should take it down. Need not count for Weaknesses.

Contest Moveset

A good Contest Moveset for Blissey would have to be this for the Beauty Contest best with Modest, Mild, Rash or Quiet Nature:

Attacks:

Hail
Ice Beam
Softboiled
Heal Bell

Items Attached:

Blue Scarf

Strategy Using Blissey

If you do the attacks in this following order you should have very few problems; 1st - Hail, 2nd - Ice beam, 3rd - Hail, 4th - Softboiled, 5th - Heal bell

Locations in Games

Ruby/Sapphire Trade from FR/LG Colosseum Trade from FR/LG Fire Red/Leaf Green Evolve Chansey

Animé Appearences

Blissey has had a couple of Animé Appearences. All in Pokémon Centers, it is in the service of Nurse Joy and it helps in the Daily Pokémon Center routine. Episode 131: Ignorance Is Blissey! Episode 173: Power Play!