Why wouldn't you take advantage of everything your platform gives you? This goes for your OS as well as your infrastructure.
There are definitely some PaaS-type offerings they have that aren't as scary (RDS/MySQL, for example, and ElastiCache/Memcached, etc.), but if you're trying to bounce systems between clouds, or deploy the exact same configuration everywhere you're running, the only real answer is to rely on compute resources (basically EC2) and build your own stuff. All the clouds have Linux servers.
The AWS services I use without hesitation are EC2, Route 53, S3, SNS (to mobile devices, not to my applications), and SES. RDS and ElastiCache can be okay for early, pre-scaling situations, and Dynamo is okay for proving out a problem before cranking out a Cassandra cluster (but I wouldn't want to scale on Dynamo, gets real pricey real fast).
I will also heavily recommend Redshift, because it's fantastic for a lot of different offline workflows and it's a lot nicer than maintaining your own. It works well without being tied to AWS for your actual infrastructure.