There is no official wording on what moves are banned, it' ussually preset by the two people before the battle. but in general these moves/items/ are typically banned:
-Any moves that raises evasion like double team or minimize.
-OHKO moves like sheer cold or fissure.
-Mind reader/Sheer cold Articuno.
-Skramory/Blissey combination double battle.
These items tend to be banned:
- Brightpowder
- Quick Claw
- Focus Band
- King's Rock
- Focus Band
- Stick
- Razor Claw
- Razor Fang
- Lax incense
In the little cup:
-Set damage moves like dragon rage and sonicboom are not allowed.
-the deepseatooth is banned as well.
There are likely other bans people might impose, like using entry hazards, but it just depends on who you're battling. Though in nintendo tournaments, OHKO moves are banned.