TIER CLAUSE:
Use Pokemon from the equal or lesser tier that you're battling within.
SPECIES CLAUSE:
No two Pokemon of the same Species are allowed (No Lucario Armies, sorry).
NFE CLAUSE:
Pokemon that aren't fully evolved are banned.
SLEEP CLAUSE:
Only one Pokemon may be put to sleep at a time.
ITEM CLAUSE:
No two Pokemon may have the same item.
ONE-HIT KO CLAUSE:
No One-hit KO moves are allowed (Sheer Cold, Horn Drill, etc.).
EVASION CLAUSE:
No Double Team or Minimize.
"HAX" ITEMS ARE BANNED:
No Brightpowder, Quick Claw, Focus Band, or King's Rock.
SELF-KO CLAUSE:
If both players have one Pokemon left, and one uses Explosion, KO'ing both Pokemon, the user of Explosion loses.
FREEZE CLAUSE:
Same as the Sleep Clause, except with Freeze.
These are some common ones, so just ask your opponent what clauses they want to use, and battle accordingly. Always organize a battle on Wi-Fi before you just run into it. Otherwise, you'll probably do something illegal. =]