My first complete Android application was an Imgur browser. This application was both written and designed alone, and took many many hours to complete.
It was a fun challenge, and filled a gap - as Imgur LLC had not yet provided their own mobile application. Around August of 2013, I pulled this app from the Google Play store as Imgur had finally provided their own solution. In the months leading up to their own release, there were sporadic breaking changes to their developer API which caused crashes across the board for all third party solutions -- which made it difficult to maintain a healthy rating in the Play store. In the end, I was able to build a product on my own, with well over 110,000 downloads, and above a 4-star rating.
It was a fun experience that I'd be happy to do again, given the right idea.
(I'm still on the lookout for where I may have put this source...)