This topic is for battles on DS Pokémon games.
Smogon competitive rules:

lvl 1-100

NO UBERS!!!

Evasion Clause
Moves that boost evasion (i.e. Double Team and Minimize) are not allowed.
Freeze Clause
Two or more Pokémon on a team cannot be frozen at the same time.
Sleep Clause
Two or more Pokémon on a team cannot be asleep at the same time. Self-induce sleep via rest does not activate Sleep Clause.
OHKO Clause
One-Hit KO moves are not allowed.
Species Clause
Two or more of the same Pokémon may not be used on the same team.
Self KO Clause
If both players have only one Pokémon left, moves which KO both the user and the opponent are not allowed (e.g. Explosion, Destiny Bond). If recoil damage would cause a tie, Self KO Clause does not activate, and the player who last attacked is the winner.
Item Clause
All Pokémon on a team must hold different items. This is not a standard clause in competitive play, but it is used in Nintendo tournaments.

List of Ubers: http://www.smogon.com/dp/tiers/uber

Leave codes if you want to battle.

You forgot the most important rule.
NO HACKED POKEMON EVAR!
There are also some optional rules like the SkarBliss Clause (in which you aren't allowed Skarmory or Blissey on the same team) and the Luck Clause (in which you aren't allowed to use any items, moves or abilities that increase critical hit ratio).
Some players can be downright annoying when they want you to abide by so many crazy rules.
One guy who wanted to battle me went batsh...MAN insane when one of my Pokes had an OT with 1337 in it (I imported it from Fire Red when getting different starters and tutoring moves onto some of my Pokes so I could chain breed them). He was all "OMFG YOU H4CKED THAT POKEYMON IM GONNA GIT U B& FROM BATTLING FOREVAR!!!1!1ONE!"