We were there 4/6-4/10 (just back yesterday afternoon)
We typically do not go this time of year...DS is not in school yet so we take advantage of going when it's less crowded. However, this trip, we met up with in-laws who are from Seattle area. It was their spring break last week. I believe there is a 6 week spread or so throughout the country for spring breaks. Ours was the last week in March and from what I understand, it sounded like the busiest week for spring break. I believe this past week has been spring break for parts of Florida, Michigan, Washington, Louisiana, Kentucky and a few other states.
At any rate, the crowds were high, but we expected it.
My advice is to really hit the parks right at opening. Beware that it is a madhouse getting in, in particular at MK. The line for the monorail was out of this world and I believe they were ID'ing people to ride the resort monorail...meaning, you couldn't ride that monorail unless you were staying at a monorail resort. I have never seen that before, maybe others have. We waited for the ferry (probably not the best way to go). We waited for 3 to come and go I believe. It really took 1 hour time between arriving at the park and actually getting through monorail/ferry, bag check, the ticket gate and heading towards a ride. Beyond that, early in the AM, you could do the rides fairly well...the lines for something like Peter Pan was 20-30 (again, this was early AM). Fastpass return times around 9:30 or 10:00 were for around 11:00 or 11:30, not too bad. Towards 11AM lines would have been 60-80. The line for Indy Speedway first thing in the morning was about 25 minutes versus 60 at around 11AM.
Another piece of advice is if you are eating breakfast early, hopefully you will be hungry early. We tried to get to a counter service restaurant before 11:30, usually around 11:15 or 11:20 otherwise the lines were pretty long too. It worked out okay for us. We would then try to ride a ride using fastpass after lunch, then back to resort for swim/nap.
Evening lines were pretty long too.
All in all, it was a little unpredictable though. We walked right onto Journey into Imagination at around 10am, and then directly after that, saw the line for the EPCOT ball ride at around 60 minutes wait. It was a little strange. Soarin' fastpasses were long gone by afternoon.
Good luck...hopefully it will be lighter than you think. Also, our inlaws found MK was EMPTY Sunday AM. It poured Sunday afternoon, but the AM was reasonably nice and like I said, they thought it was totally empty. Maybe a lot of people were coming and going so no time for parks???
Get there early!!!