It sure can!: http://aws.amazon.com/autoscaling/
If you're thinking alternatives, Rackspace can as well but not automatically; you'd have to watch your servers and use the api to add/remove servers.
I prefer Rackspace myself but mostly because it's what I'm used to.
However, if you're not looking to start/stop new instances, and in fact are looking to just have one instance that scales up and down as required, you would be limited to writing your own scripts and using the API but could definitely do it. With that said, Rackspace only requires one API call to resize a server. Amazon requires 3 (shutdown, resize, startup), which is a problem if you're only using one server (since it'll be offline after the first api call). Note that resizes are NOT instant so if done this way there would be downtime (again, unless you use more than one instance.)