I came across this forum thru a search for an app to read rtf files on my android phone. I was shocked to see that this question was asked a year & a half ago & here I am w/ the same problem. What's up, Google?
Anyway, in case anyone else stumbles across this forum w/ the same question, I thought I'd post that I FOUND AN APP TO READ RTF FILES. Like someone mentioned above, so often w/ Google Play this happens by accident.
There were a lot of suggestions above. Some were too specific & not a solution for the original problem: the need to view & EDIT rtf files. So that eliminates readers such as CoolReader or Multireader. I never found an app called File Share in Google Play.
The other problem for me personally is I like free apps. So that eliminated Documento, Multireader, and DEFINITELY OfficeSuite Pro, which is $15! At $15, you better be writing my docs as well. But that's just me.
So, while browsing, I came across OfficeSuite Viewer 6. It's free, and I viewed my files beautifully. I haven't tried to do anything else yet, so I can only say that. This is a true and FREE solution. Yay! (I only wonder why that was so hard to find!)