Like most elements of negotiation, it might go either way. If you're some fresh out of high school Janitor, you'll have a hard time negotiating for personal projects. If you're one of a handful of people with a certain skillset, then companies will be happy to cater to far more outlandish demands.
In my experience, this sort of thing isn't common. Training is often already handled by the company, and (contractually) treating you specially isn't worth the minor benefit of your increased value/productivity. Some companies see that sort of thing as something you should do on your own. And not a few companies simply won't negotiate, since paying the lawyers to validate the contract is more time/money than finding another acceptable candidate (who is happy not negotiating).