I'm not sure if there's an exact limit, though I do know that the more tiles you put on a dashboard the longer it may take to load. I personally have a few dashboards with more than 40 tiles.
Limit - if exsist - is very high. From my experience I would say big amount of tiles can slightly impact on server performance.
Just like coulleage wrote above, I have many dashboards with 50 or more tiles.