Battle Moveset

A Good Moveset for Regice would have to be this:

Attacks:

Ice Beam
Thunderbolt
Thunder Wave
Explosion OR Rest

Items Attached:

Leftovers

Preferred Nature:

Calm

Strategy Using Regice

Being one of the few ice types in the game, it has only one resistance; ice types. As you may notice, Regice's special defense is very high and it will survive the majority of special moves used against it (you could add Amnesia on Regice to boost this even further, though this could just trigger a switch to a physical sweeper that will defeat the purpose of a special wall)
Its special attack isn't too bad either, allowing it to use Bolt-Beam, which as stated in the counter, is only resisted by Magneton and Lanturn.
Thunderwave will certainly make up for the lack of speed when it reduces your opponent's speed in half and gives you a 25% chance for a free turn or it may force your opponent to switch.
Even though Regice may have a low attack stat, Explosion will still do a lot of damage. Rest is another possibility, since the nature is usually minus attack.

EV Corner:

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

Strategy Against Regice

Regice is potentially the best Special Sponge available. When caught of guard with a Physical Attack it can survive it and it has Average HP and well above average Special Defence. It has the Bolt-Beam combo (which is only resisted by Magneton and Lanturn) and also access to Thunder Wave which can be incredibly annoying.
- Firstly, don't expect to automatically knockout Regice with physical attacks. Even without defensive EV's it is more than capable of surviving them (unless you are attacking with very high base attack and a Fighting, Steel or Rock attack). A Pokémon such as Machamp (who can outrun Regice even with such low speed) using Cross Chop can put a pretty bad hurting on Regice's HP.
- Alternatively, you could stall with Thunder Wave and Confuse Ray and slowly pick away at Regice, although this may take a while and you are at risk of losing all your efforts to Rest.
- Obviously, there is also the Seismic Toss and Night Shade options available, which will KO Regice in 3-4 hits, although this is pretty slow and leaves you exposed to it's offences, so this is best done with some form of stalling in use.

Contest Moveset

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

Attacks:

Hail
Ice Beam
Blizzard
Explosion

Items Attached:

Blue Scarf

Strategy Using Regice

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

Locations in Games

Ruby/Sapphire/Emerald Island Cave on Route 105 Colosseum Trade from R/S/E Fire Red/Leaf Green Trade from R/S/E

Animé Appearences

Regice has yet to have an appearence in the Pokémon Animé or Movies