Each edition has different rules with respect to this. The easiest way to find out is to look up the class you're interested in and whatever edition you are playing. 

For instance: Google search 3.5 Monk to find out that Monks need to be any lawful category.

As an example, D&D 3.5 has alignment rules for several classes such as Paladin, Barbarian and Druid. 

Barbarians (any non-lawful); Paladins (lawful good); Druid (any neutral)

D&D 5e removed all restrictions and made alignment a general thing for characters. There is flavour text indicating which classes tend to do what, however the customization aspect allows for things like chaotic-evil Paladins.