Inconsistent - at the end of each turn (including the turn the Pokémon was switched in), randomly increases one of its stats by 2 stages and decreases a different stat by 1 stage (including accuracy and evasiveness). Inconsistent cannot attempt to boost a stat at +6 or lower a stat at -6 (it can still lower +6 and raise -6, though).
Pokémon with this ability:
This ability was overlooked at first, with many people claiming it to be inferior to the Pokémon's existing abilities (Suction Cups, Simple etc). However, Inconsistent has recently made a comeback, with its users even being discussed in the Suspect Testing thread. Why?
Simply because Inconsistent has a 1/7 chance of sharply increasing the user's evasiveness; a pseudo-Minimise. And we all know why Minimise is banned - after even a single boost, the Pokémon becomes difficult (and very annoying) to hit.
Inconsistent's second advantage over moves like Minimise and Acupressure is that it happens automatically at the end of each turn, freeing up your move choice. By far the most popular option here is stalling an opponent with Protect and Substitute; a switch in followed by Protect gives Inconsistent two chances to activate; if it boosts Speed or evasiveness, you're pretty much set. Leftovers is the preferred item here for the increased number of times you can use Substitute. An Acupressure or Minimise user is vulnerable during the turns it sets up; an Inconsistent user is not.
Ingrain-passing Smeargle greatly helps Inconsistent users, providing them with a second source of healing (allowing them to spam Sub + Protect until they run out of PP) and preventing them from being Roared / Whirlwinded out. However, it also stops them switching out against Unaware users, which can easily set up on them (Cosmic Power Clefable and Curse Quagsire or Bibarel).
Toxic Spikes are a great help, as they wear away the opponents' HP as you set up. They also mean you can run two attacking moves instead of one attack + Toxic, which means you have more type coverage and can avoid being walled.
However, Inconsistent also has its counters. As with any stat-increasing strategy, the moves Haze and Clear Smog are useful - Clear Smog also has the bonus of being a never-miss damaging attack, getting past Inconsistent's evasiveness boosts. Morobareru (the new Poké Ball mushroom) can learn Clear Smog, resists Water (the most common Inconsistent user attacking type), and is immune to Toxic, making it a great counter to the two available Inconsistent users. Murkrow, despite being NFE, gets good defensive stats through Evolution Stone, and can wipe the slate with a priority Haze (thanks to Mischievous Heart).
Roar and Whirlwind can work, but watch out as they can miss if the Inconsistent user has evasiveness boosts. These won't work against Ingrain Smeargle either.
Taunt blocks the opponent from stalling, but if the opponent has a few Attack boosts, it won't really help you otherwise. It also doesn't block Inconsistent's effect, so they'll still be getting stat boosts.
A Pokémon with Unaware, such as Quagsire, Clefable, or even opposing Bibarel, can ignore the Inconsistent user's defensive and evasiveness boosts, while taking measly damage due to ignoring their offensive boosts. Quagsire can even use Haze. However, all Unaware Pokémon have to beware of Toxic stalling movesets.
Pokémon with the ability Trace such as Porygon2 can switch in and set up alongside; as Trace users generally have higher stats than Inconsistent users, this can be quite an effective strategy. However, this shouldn't be left for too long after the Inconsistent user comes in, to avoid it getting too far ahead in stat boosts.
Heart Swap Manaphy yoinks the opponent's boosts, leaving them with nearly nothing. Its only problem is that it's not very useful against anything else.
In the Dream World metagame, if the Inconsistent user's (Sp.) Def stage is lower than their (Sp.) Atk stage, and their accuracy is at least as good as their evasiveness, Ditto can come in after their Sub is broken. However, they'll most likely set up Sub again, which would be troublesome to beat. Also, you could get screwed over if they get a Speed/evasiveness boost on the switch. Just make sure you don't switch Ditto in on a Sub.
Sandstorm and Hail severely limit the survivability of Inconsistent users, which usually rely on Substitute to avoid getting hit. Glalie (when it is released) is immune to Hail, however.
Speaking of Hail, Stallrein (and other stallers) can PP stall Inconsistent users out of Protect / Substitute PP; however, they still have to watch out for +6 Struggle!
Toxic Spikes also cripple Inconsistent users in the same way as damaging weather, hugely reducing the amount of time they have to set up.
Finally, Perish Song is useful for countering Inconsistent users, either KOing them or forcing them out. A switch is nearly as good as a KO, as their Protect and Substitute PP will have been depleted, meaning when it comes in again, it won't be able to stall for too long.
The most popular available Inconsistent user is Octillery, due to its higher stats and lack of a Fighting (and therefore Aura Sphere) weakness. Here is a common Octillery set:
Octillery @ Leftovers
4 HP / 252 Sp. Atk / 252 Spe (Sp. Atk EVs can be moved to HP for a bulkier set)
Timid nature
-Protect
-Substitute
-Surf
-Toxic / Energy Ball
Timid nature and max Speed, despite its low Speed stat, allows it to outspeed many slow Pokémon. This means it can set up a Sub and start stalling; once it has a few evasiveness or defensive boosts, and its Sub is intact, it can start attacking or statusing opponents.
The most popular way to use the set is to switch it whenever possible and Protect; if you get a Speed or evasiveness boost, start stalling with Sub + Protect; if you don't, switch back out. This strategy is weakened by entry hazards, however.
This particular set with Toxic is walled by Toxicroak and RestTalk Suicune. Also watch out for Water Absorb/Dry Skin/Storm Drain users coming in and Subbing while your Speed is low. Energy Ball allows you to beat them, but in turn, you're walled by Shedinja. But seriously, with Toxic Spikes support, Energy Ball is superior (even without, it's pretty good, though it leaves you reliant on getting Sp. Atk boosts).
Bibarel and Glalie tend to use similar sets; both are faster than Octillery, though less powerful (not like it matters when you have +6 Attack). Glalie has slightly higher defensive stats, but this is ruined by its pure-Ice typing. Bibarel can run Taunt, but then only gets one damage-dealing move; only use it with Toxic Spikes support.
Smeargle, on the other hand, likes to use a Baton Pass set. This set can beat many of Inconsistent's usual counters:
Smeargle @ Leftovers
252 HP / 4 (Sp.) Def / 252 Spe
Timid nature
-Protect
-Substitute
-Baton Pass
-Taunt / Magic Coat / Gear Change
Protect and Substitute are again to stall for boosts. If your opponent sends in a Clear Smog user, Baton Pass to a Steel type; as Clear Smog is Poison, your stats will be safe. If your opponent sends in a Haze/Roar/Whirlwind/Taunt user, Taunt them back (watch out for Mischievous Heart Pokémon like Murkrow and Voltolos, though).
Magic Coat is an alternative for stopping Taunters and phazers. It's useless against Haze, but lets you beat Mischievous Heart Taunters.
Gear Change makes it easier to stall by boosting your Speed. You'll probably want Magic Mirror Espeon / Xatu to BP to against Taunters or phazers, though. Again, it's beaten by Haze.
Alternatively, you can run an Ingrain-passing set; this allows you to stall until you run out of PP (as Lefties + Ingrain heal back the health lost by Substitute over the two turns you use Protect and Substitute). This is especially evil if you pass to another Inconsistent user such as Octillery.
If you're still doubting Inconsistent, have a look at these logs by Stellar. With a bit of luck, Inconsistent becomes very hard to beat.
Wouldn't it be funny if Bibarel became Uber?