I am running a massive Rails app off AWS at this time and I'm really happy with it. Previously I had a number of dedicated boxes that were always causing problems - sooner or later one of them would crash for some reason, Raid failures, database problems whatnot.
At AWS I use RDS for database, elastic cache for caching, I keep all my code on a fat instance that acts as staging server and get a variable number of reserved instances to load the code via NFS.
I also use autoscaling - we've prepaid for a number of reserved instances and autoscaling helps starting up nodes when CPU usage goes above 60%, then removing them when it goes below 25%. autoscaling rules are based on cloudwatch alerts that can be set to monitor a particular group of instances, memcache servers, and so on, you even get e-mails and SMS notifications via SNS when certain scaling activities take place, say when more than 100 instances are spammed in less than 1 hour (massive traffic spike). The instances also get added right up to the load balancers by the way and you don't need to mess with the session store as you can use the sticky session feature which is quite nice.
Recently I also started using a 2nd launch group with spot instances, this complicated things a bit in terms of cloudwatch rules but I'm able to save a lot every month as spot prices are much lower. When the spot price (minimum) I bid is not enough, the set-up I have switches back to reserved instances.
Even more recently I've also started using CloudFront which got my app's page assets to load real fast (about 2 megs of CSS, JS, some icon sprites). Previously I was serving directly from instances via the load balancers.
This took about 20 hours to deploy, test and tune for maximum performance and availability.
One of the problems I have with AWS is that there's no support unless you're prepared to foot a bill. They claim some support is offered without a subscription but the only option in the support area is Billing. Ha. Fortunately it's all stable enough not to put me in a position where I'd have to pay for it.
Overall Rails fits in quite nice with AWS. I spend less than 2 hours per month doing maintenance, where I was spending over 30 previously. Most important for me is that I know that I can GTFO on a vacation for X months knowing nothing will cause any trouble - haven't had a monitoring alert more than a year.
Later edit: the app is a sports site with white labeling feature, lots of users, lots of administrators working on content in the back-end, database intensive as we show market pricing data that should update every few seconds. I had an average load time of about 3 seconds per page with dedicated servers that were doing about the same thing - database, memcache, storage, load balancing, web app. Now my average is under 1 second. Monthly bill is about 8 times lower now.