The max level is traditionally 100, however, in Mega Dimension PLZA's DLC, you can encounter Pokemon up to level 200.
Additionally in the first two generations, there were several glitches the could apparently get your Pokemon to 100+ levels. Bulbapedia does not state the level-changing effects of the Pokemon Merge Glitch mentioned in another answer on this post, but the answer does mention the effects of that and also the Old Man Glitch.
By exploiting the old man glitch in Generation I, a Pokémon can be acquired at a level higher than 100. Also in Generation I, any Pokémon can also be raised to a level above 100 via the Pokémon merge glitch; however, Pokémon in the Slow experience group need to be merged with a glitch Pokémon who requires even more experience at level 100. These Pokémon can continue to be leveled up with Rare Candies until level 255. Whenever a Pokémon over level 100 gains any amount of experience, its level will revert to 100, and if a Rare Candy is fed to a level 255 Pokémon, it will revert to level 0.
Source: experience
Hope I helped!