All of the status effects that take away control of a character can wear off over the course of a battle. They take up the turn they wear off on. The effects that don't take control away don't wear off during a fight.
Sleep prevents the victim from taking action. It also prevents the victim from dodging attacks while it is asleep. It naturally wears off either during or at the end of battle, but can be cured prematurely with the Awake spell. A sleeping target has a 1/2 chance of waking up each turn in battle.
Stopspell prevents spells from being successfully cast. It lasts until the end of the fight with no other known cure.
Surround sharply reduces the chance a physical attack will hit. It lasts until the end of the fight with no other known cure.
Chaos causes the victim to either stand around confused, help his enemies, attack himself, or attack his friends. It naturally wears off either during or at the end of battle, but can be cured prematurely with a Full Moon Herb. Each turn, a confused target will randomly choose one of four actions (probability of each action may or may not be equal): Cured, Physical Attack, Cast Spell, Do Nothing.
Paralysis prevents the victim from taking action. It also prevents the victim from dodging attacks while it is paralyzed.
Paralysis can wear off during battle and during travel. To cure it prematurely, either the Numboff spell or a Full Moon Herb can be used. Note that Paralysis does not automatically end with combat but overworld travel will usually cause it to wear off. Each turn, a paralyzed target has a 1/8 chance of being cured.
Fear prevents the victim from taking action for one turn. It also prevents the victim from dodging attacks while it is frozen with fear. It uses the same resistance value as paralysis, but it has a multiplier somewhere in the formula to make it harder to resist. Some monsters may be immune to howl.
The damage done by poison is MaxHP/16 OR 1 HP, whichever is greater. This damage takes place immediately after the afflicted one's action. Traveling while poisoned inflicts damage comiserate with the distance traveled. (It has been suggested that doing anything that takes a substantial amount of time will cause poison damage.) Poison does not wear off. It can be cured with either an antidote herb or the Antidote spell. Churchs in towns can also cure poison.
Can cause various effects depending on what caused the curse. To fix it, a trip to the Hexologist is required.