I'm the sole developer on a web application project that a friend and I started up. I'm handling development and my friend is handling the business side. It's a guerrilla operation and with what our application is trying to achieve I could never develop it on my own in a reasonable time. So I'm planning on using many services to run the application. AppFog for hosting and deployment, MongoHQ for the database, Searchify for document indexing, Filepicker.io for file uploads, and AWS for misc utility needs. Besides the obvious worry about one of these companies going under, are there any other reasons why I should absolutely not be doing this?
I figure if our application actually takes off and we make any kind of revenue, at that point, I could then put resources into building solutions to take the place of different web services I'm currently using.
then you should be OK.
I don't think using many services is bad in itself - it's neither productive nor reasonable to build everything by yourself.
You definitely want to leverage what is out there, but protect your core competencies.
The earlier point about building in flexibility in case you need to swap providers is a very good one. In Object Oriented design, that is called an abstraction layer. Your tech team should design for flexibility and anticipate swapping things out down the road.
Also consider how slow the site will load if the back end jumps off to half a dozen APIs spread out all over the cloud.