I have to agree with ResidentBiscuit on this one. Without knowing skill, experience, or interests we can't narrow it down for you. One would assume that since you are in the C++ site that you are wanting C++, but for all we know you could be doing Python, Perl, Ruby, Haskell, C, D, HTML5, etc. We don't know your interests so we don't know if you want game programming, web dev, networking, GUI programming, etc. Experience, without that we don't know whether to tell you Pong, simple RPG, FPS, Word program, web browser, irc client, etc.
pull a richard stallman and rewrite all of the programs in the gnu /bin folder. thats a good starting point and teaches a lot of general techniques, like file io, regexing, networking, system level api
write a simple c program that keeps yours files synced up, for example I wanted all my music synced from one pc to a external drive. I think that was one of my first project. Something like DTSCode said, when starting out its better to try and recreate something that already exists just put your own spin on it.