Is there a limit on how many Ad Groups you can have for each AdWords campaign? I know there are caps of 25 campaigns and 50k keywords per account.
The limit of adgroup per campaign is 100, but it can be raised to 10,000 adgroups per campaign by contacting support.
There isn't a limit of 100. I've got over 140 in a couple of campaigns and never had to ask for permission, the groups just 'grew' as I split them to make the ad fit more and more tightly, and added new things.