Status Ailments
Status ailments are icky things that are inflicted by various Pokémon attacks. Some go away on their own, some do not. It is important to know how to deal with and prevent status ailments, because they can debilitate even the toughest Pokémon.

First of all, the list of ailments.

Burn is a serious ailment that reduces your Pokémon's Attack stat by 1/2. It also causes your Pokémon to lose 1/8th of its max HP every turn. Fire-type Pokémon cannot be burnt.

Freeze can render a Pokémon useless until it is cured. Freeze does not affect stats or do damage, but it prevents the Pokémon from making attacks. Only the following moves may be used by Frozen Pokémon: Flame Wheel, Sacred Fire, Flare Blitz, Fusion Flare, Scald, and Steam Eruption. These moves will cause the Ice to melt (and the attack goes through in the same turn). The Freeze status can also be removed by allowing your opponent to strike the Frozen Pokémon with a Fire attack. (Obviously, you would have to trick him or her into doing that for you.) If a Pokemon is frozen, there is a 20% chance of it defrosting each round. Ice-type Pokémon cannot be frozen. Pokémon cannot become frozen in harsh sunlight.

Paralysis is the most popular and debilitating ailment in use. Paralysis has two effects; one, the Pokémon's Speed is cut to a quarter of its original value. Two, the Pokémon has a 25% chance of being 'fully paralyzed', meaning it misses a turn. Electric-type Pokémon cannot become paralyzed.

Sleep is a very dangerous ailment. Some official tournaments, as well as many trainers, use the 'Sleep Clause' - only one Pokémon may be put to Sleep at a time. That Pokémon must awaken or faint before another can be put to sleep, otherwise the opponent loses by default. Sleep can last from 1 to 3 turns - the counter is reset if the Pokémon switches out -, during which time, your Pokémon cannot attack. The only moves it can use are Sleep Talk and Snore. In addition, the moves Dream Eater and Nightmare can only be used on Sleeping Pokémon.

Poison is the classic Health-lowering technique that has been refined into a science over the years. Poisoned Pokémon lose 1/8th their max Health each turn (1/16th in RBY) and also take a point of damage every four steps out of battle. A few moves, like Toxic, can inflict 'bad poison' which starts at 1/16th in all versions, but the damage done increases by 1/16th each turn as time wears on. If a badly poisoned Pokémon switches out, it is still badly poisoned, but the counter will reset. If a Pokémon with the Synchronize ability becomes badly poisoned, so does the attacker. Poison-type and Steel-type Pokémon cannot become poisoned.

Confusion is not considered a 'major' ailment because it does not change your status, thus, your Pokémon can be Confused as well as Burnt, Paralyzed, etc. Once Confused, your Pokémon has a 50% chance of hitting itself. No matter what the attack (even if a damaging attack was not chosen), if your Pokémon hits itself, it does it with a 40 power Physical attack that takes no particular element. It does not Critical Hit. Confusion lasts from one to four turns. Confusion is second only to Paralysis as the most irritating ailment, and even worse is to get hit with both at the same time (sometimes called "Parafusion"). While switching can remove Confusion, you're still giving your opponent a free hit.

Now that you know the five major ailments, you should check the following information for ways to prevent and heal them.

Safeguard is the optimal ailment-preventing technique. It does not heal them, but for five turns (including the turn used), your entire Pokémon team is shielded from all status ailments, including Confusion.

Substitute can protect the user from all Status effects until it breaks. It can also be passed to other Pokémon with Baton Pass.

Heal Bell is a very rare technique that can cure your entire team of Burn, Freeze, Paralyze, Sleep and Poison. It cannot cure the user of Sleep, however (through the use of Sleep Talk). It does not affect Confusion.

Rest can cure the using Pokémon of Burn, Paralyze and Poison. It has to be used to work, so obviously, Frozen or Sleeping Pokémon cannot use it. In addition, the using Pokémon falls asleep for three turns.

Refresh cures Poison, Burn and Paralysis.

Haze removes ailments in RBY only. In later games, it does not, nor does it affect Burn or Paralyze's Attack or Speed cuts.

Sunny Day will prevent Pokémon from Freezing.

Items like Burn Heal, Antidote, the Poké Flute, and Full Heal can be used to cure major ailments in-game. None of these can be used in link battles, however.

Though it is little consolation, Fainting will remove all afflictions from a Pokémon. Big deal, as there's no way to revive them in a link battle.
Some notes...

A Pokémon cannot have more than one major status ailment at a time. If a Pokémon is Burned, it will never Freeze. A Sleeping Pokémon cannot be Paralyzed. However, Confusion is not a major ailment, so it can be used if another ailment is already in place.

If an element is completely ineffective against another element, a status inflicting move may not work- Ground types will never be affected by Thunder Wave. However, for some reason, Normal and Ghost status attacks work on each other. (Confuse Ray, Sing, etc.)

Attacks have to hit before the ailment chance can be considered. Smog has a 39.8% chance of Poisoning but only a 69.5% chance of hitting, thus, its true Poison rate is only about 27.55%.
Thanks to Uiru's Pokémon DataBase for the information on this page.