Question

What is the maximum number of turns a Pokemon can be frozen/asleep?

Answer 1

Sleep:

Gen I: 1-7 turns (random) [Stadium: 1-3]
Gen II: 1-6 (random); 1-3 in Battle Tower
Gen III: 2-5 turns (random)
Gen IV: 2-5 turns (random)
Gen V+: 1-3 turns (random)

Source: Bulbapedia/ Sleep

Frozen:

Gen I: Will only thaw via Ice Heal, and opponent using Haze, or getting hit with a Fire-Type move that can burn. So the Pokemon can be frozen indefinitely.
Gen II: 25/256 (~10%) to thaw every turn the user attempts to move. So freeze can still last indefinitely.
Gen III+: All Fire-type moves now thaw their target, and the per-attempt thaw chance is increased to 20%. But there is never a point where a Pokemon is guaranteed to thaw.

Source: Bulbapedia/ Frozen

Comments

Your answer is better than mine for sure. LOL we used the same source.

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i know this is old but this is why i dont use bulbapedia. for the sleep your mostly correct, mostly cause its not really random its a chance every turn to wake up, starting with a slim chance and escalating to a 100 % chance on the last turn. lets take current sleep for example, current sleep works as turn 1 has 0% chance to wake up, turn 2 is a 25% to wake up, and turn 3 is a 50% to wake up with turn 4 having a 100% wake up chance. though this is predetermined in usum when you enter battle. thats all i have for sleep, as for freeze, in gen one its any fire type attack move that can burn, not just any fire type attack move. that little inclusion is needed cause fire spin cant burn and will never thaw a frozen pokemon. like how body slam cant paralyze normal types in gen 1 (yes, thats an actual thing)

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@League of Legends How do you know this?

E: Bulbapedia does include the information about Fire-type moves that burn, but it was missing at the time this answer was written. I will just update it. I would be interested to see proof this was known a long time before it was added to Bulbapedia.

Answer 2

Freezing

Damaging Fire-type moves used on a frozen Pokémon will remove the freeze status. From Generation II onward, freeze has a random, 20% chance to be cured on its own on the frozen Pokémon's turn. Consequently, the frozen Pokémon may thaw out on the turn of freezing; however, in Generation I, a frozen Pokémon never thaws without external aid. Pokémon cannot be frozen in sunny weather; contrary to popular belief, sunny weather does not cause a quicker thawing.
Source: http://bulbapedia.bulbagarden.net/wiki/Status_ailment#Freeze

Sleeping

Sleep lasts for a randomly chosen duration of 1 to 3 turns in Pokémon Black and White and Pokémon Stadium.[1] In all other games, except the Japanese versions of Pokémon Diamond and Pearl, sleep lasts 1 to 5 turns. In the Japanese version of Diamond and Pearl, the minimum and maximum sleep count is 1 turn higher, lasting 2 to 6
Source: http://bulbapedia.bulbagarden.net/wiki/Status_ailment#Sleep

Unless you have Early Bird which causes your Pokemon to wake up faster.