By law, how much can a landlord raise your rent in a year?

The only state that I'm aware of that has limits is Calif. so other than that, rent can be raised as high as the landlord likes as long as you don't have a current lease.

Except in those areas that have rent control, they can raise them to that amount that the market place can handle. 10 to 15 percent is very common his year.

In NJ the increase must be "reasonable". If a landlord increases the rent by more than 20% you might have a very good case that it is not reasonable.