Yes, it's possible to design an application to either not use a database at all, by storing _all_ your data on S3, or to implement some workarounds that deal with DB master-slave replication, store commit logs on S3, etc etc etc. Question is: is it worth it? In my opinion, no.
S3 is great if you want to store images, movies, etc and aren't very popular worldwide. EC2 is great if you need extra processing power to deal with extra traffic coming from those Digg/Slashdot stories, or doing batch processing like converting movie formats, but going 24/7 on simple EC2 or EC2+S3 (using S3 as a database and not just for storing media files) is more of a hassle than a "good enough" solution. VPS is definitely the way to go if you cannot afford to lease a couple of servers or some rackspace for the cheap 1u boxes you can buy at ebay.