Garry's Mod maximum amount of addons/mods
Solution 1:
As far as I know, the only limit is your computer's performance!
EDIT: As @Codingale pointed out in his answer, there is in fact a limit.
Solution 2:
Yes there is somewhat, not a limit of what content or anything however there is a limit on how many Lua files may be loaded at once.
https://github.com/Facepunch/garrysmod-issues/issues/1058#issuecomment-46835256
The current limit seems to be 4096. I doubled it so it should now be 8192. If that didn't change anything let me know, maybe there's another hardcoded limit within the engine and it might be a bit more tricky to remove.
So you can have as many addons so long as the number of Lua files does not exceed 8192.