Oh my GAWD, during the World Series a few years back it was HORRIBLE. If it wasn't for the interesting celeb-watching, I would have pulled my hair out. Plus I only had one kiddo with me. There were two days that we barely went on rides at all. We just gave up. She was 4 and not up to the extremely long lines and all the fastpasses were long gone early each day. Not fun.
We were there during the Angels/Giants series too. In fact, since the DL Hotel was booked, we got a room at the Marriott. Well, us AND the Giants! They booked the entire first floor for their team and related personnel. After we were there for two days (with 4 to go), the hotel asked us to change rooms (we were on the first floor, towards the rear of the hotel). We refused, since we had a handicapped room and needed the patio door which lead out to the parking area. They were not happy, but I think they were afraid to push the issue due to the handicapped situation. The kids got plenty of autographs and pictures of the players. We watched them load into the bus a few times.
Remember the rally monkeys??? They were EVERYWHERE!!!