Standard Battle rules are what most 'competitive' battlers play by. These are used to keep the battle fair and balanced.
When accepting a Standard battle you agree to all the following rules:
No Ubers
Neither player is allowed to use any uber Pokemon as they are much more powerful than the Pokemon in the below tiers. The most common list of uber Pokemon is the Smogan(A big Pokemon website and community) list.
The Uber list is as follows:
Arceus
Darkrai
Deoxys
Deoxys-A
Deoxys-D
Deoxys-S
Dialga
Garchomp
Giratina
Giratina-O
Groudon
Ho-oh
Kyogre
Latios
Lugia
Manaphy
Mew
Mewtwo
Palkia
Rayquaza
Shaymin-S
Wobbuffet
Wynaut
Sleep Clause
You can't use any sleep inducing moves on the opponent's Pokemon when there is another Pokemon in his/her team asleep (this includes moves like yawn even though it does not instantly cause sleep). This only counts for sleep that you have caused, sleep caused my moves such as rest is excluded from this rule. Once a sleeping Pokemon has fainted or awoke you are free to use a sleep inducing move but the same rules apply each time.
Species Clause
You can't use two of the same Pokemon in a team.
Evasion Clause
You can't use moves that increases your evasion such as Double Team.
OHKO Clause
You can't use any OHKO (One hit knock out) moves. They are Guillotine, Horn Drill, Fissure and Sheer Cold.
No Hacks
Hacked Pokemon of any kind are banned even if hacked from hacked parent, whether their stats are realistic or not. Obviously there is no way to guarantee this so players have to trust each other to use legit Pokemon.
No Hax Items
These are all the items that rely on luck to activate. These items are: Brightpowder, Focus Band, King's Rock, Lax Incense, Quick Claw, Razor Fang, Lansat Berry and Lucky Punch. Scope Lens, Razor Claw and Stick are also considered hax items but they are allowed in competitive play, as they just increase the odds of something that can already happen.
No Disconnecting
Do not turn off your DS or deliberately move out of your Wifi signals range to disconnect from a battle. However do not assume all disconnections are deliberate as people can have weak connections or other problems that cause this.
For more information on other rules people play by and the associated tiers, have a look at the following pages on the main site:
Battle Rules:
http://www.pokemonpwns.co.cc/BattleTypes.php
Tier Lists:
http://www.pokemonpwns.co.cc/TierLists.php