What happens when stats go above the "max"?

I've read on some guides that certain stats have a max (usually 50). My apprentice is level 37 and has a tower damage stat of over 100: about 60 on the character and 40+ on equipment. Usually level ups take me by surprise, and I haven't had a chance to confirm what's happening to my tower damage when my stats go up.

Do bonuses to these stats apply indefinitely? If not, what is the hard cap? Is there a certain point at which I should stop adding points to tower damage, tower attack rate, etc.?

The max cap is just for what you can raise the stat to via leveling, not the max it can actually be. Your item bonuses and such will allow you to go beyond it and is where character customization comes into play in an extended format.

Hope this helps!