Cala, I've been to Plitvice in May and in early October. In both cases, there were plenty of tourists by mid-day, but I wouldn't call them mob scenes - not unbearable. Still, as a photographer, I greatly preferred the early morning when the park was pretty empty. I'd say May or October isn't a bad time to go. Spring means the falls are probably running a little faster after the recent rains. Fall means more color in the trees.
I've not been to Plitvice in summer, but I've read numerous anecdotes about how incredibly crowded it can be - lines for boats, lots of people on the trails. Sounds unpleasant to me. However, if you get into the park at 7am, even in summer, I'm guessing it's not so bad for the first hour or two. Plitvice really doesn't require days to see. You can get the gist of it in 6-7 hours, easily. A few uncrowded hours in the morning or maybe late in the day might make up for a busier scene during the day. Doing it as a day trip say 10am-4PM would seem like about the worst time to be there, especially in summer, because you wouldn't see the park without people around you.