I recently took a few flights between Alaska (Terminal 3) and Delta (Terminal 5). In terms of how long you need to give yourself between flights, I would suggest at least 90 minutes, and preferably 2 hours. Catching the shuttle bus is hit or miss. There were times that there was a bus there in 5 minutes. On other occasions, it took over an hour for a bus to show up. The people at the shuttle bus gate were worthless when the bus didn't show up on time. All they kept telling us was, "the bus comes every 15 minutes" even after we were waiting for an hour. On the last occasion going between the 2 terminals, I was going from Delta to Alaska with a 90 minute connection time. I had to wait over an hour for the bus to come pick us up to take us to terminal 3 (the bus ride itself takes 10-15 minutes). The only reason I made my flight was because I was flying Horizon and the flight was delayed due to the Q-400 breaking down (a common occurrance in my experience). Luckily, this whole issue will be over with when Alaska moves to terminal 6.

I would assume that the wait time between Alaska and American flights would be similar.