We went this past May (7th-16th) and the weather was fantastic -- mid-80's during the day and mid-to upper-70's at night. There was only one afternoon with cloudy skies, and it sprinkled for maybe an hour--no heavy downpours! The crowds were low, and the most we waited for any attraction was 15 minutes (we did use Fastpass when available and necessary--Test Track and Kilimanjaro Safari were the only two really long lines during our stay).
The Flower and Garden Festival at EPCOT is in full swing then, and the topiaries are awesome to look at and take pictures of.
The nightly entertainment is never disappointing (I hope Dave Mason is back again this year)!!! Also, at MGM in mid-May, they begin Star Wars weekends. There is something for everyone.
We had our kids with us. DS had a packet his teacher prepared before we left (we gave him 2 months notice, which helped) and my son had it done before we got to WDW! DD is in preschool, so that wasn't a problem.
This is the last year that we will take DS out of school--he'll be in middle school next year (but May is the only time of year I can take vacation time from work)...we'll have to figure out when/how to schedule the WDW annual trip---we really like going in May!
Anyway, the kids were paid quite a bit of attention by the characters. I suggest still making late reservations for character breakfasts, because very few people are there and you have them practically all to yourself (not to mention that making it "Brunch" can save on meal costs)! And if you wait until late in the day, at the Judges Tent in MK the kids can have Cinderella all to themselves! My daughter had a 5-minute conversation with her and a photo session with Cinderella, Perla and Suzy!