We were there 8/13-8/16. The information board posted wait time was usually 120 minutes. The shortest posted time I saw was 90 minutes I think. I didn't check the wait late at night (after the info board shut down). It was cute, but is not worth a 2 hour wait.
Most of the EE guests went to Nemo, and the line was long immediately. I imagine it is the same way on non-EE days. I agree with the previous poster, if I had one EE, I would use it on Fantasyland, and ride Nemo first thing on a non-EE day. But I would also recommend getting to the gates AT LEAST 1/2 hour before opening.
As guests of the DLH, we had 2 EEs, so we used one for Nemo. On our Nemo day, we arrived at security before 6:30 (more like 6:20). Security didn't open up until 6:45, but I imagine if you were not in line by 6:30-6:40 you were going to be pretty far back in line when the gates open. The lines at security were longer on the Harbor side. Even though we ended up being first in line at one of the gates, and first in line for Nemo (my son moves fast), it still took over 1/2 of EE to ride Nemo since you have to walk to entire queue and it's not a short ride.
(If you are a guest at one of the Disney hotels and want to ride Nemo first thing, go to the front gate early; don't ride the monorail - it usually doesn't arrive until several minutes after the front gates open; by then the line to Nemo is very long!)
Hopefully, Nemo lines will start getting shorter now that the peak summer season is coming to an end, but they were still pretty darn long last week. I felt bad for the little ones who especially love Nemo and got their hopes up. And I really felt bad for the poor souls who waited 2 hours in the hot afternoons.