This app was mentioned in 6 comments, with an average of 2.50 upvotes
I'll add a vote for Tsumego Pro.
Also, Go Quest. If you want to play 5 minute 9x9 games against other people with good matching, it does that very well!
For quick games while on the bus I've enjoyed playing 9x9 or 13x13 games on Go Quest.
The FAQ seems to have a pretty good list of the various online servers as well. Don't think one server is better than another, they're all just a bit different in terms of ease of finding games and how people there tend to play.
Download the Wbaduk app for your phone(free) or for your computer (note the computer version is a bit laggy, so I recommend getting the app), it has 1000s of problems free at all levels. Remember that when you do problems, do not play anything until you are 100% sure of the answer in your head. Just trying out different spots will not help you read.
Also, it is very difficult for a beginner to realize which moves are good/bad on a 19x19 board, especially an equally unskilled opponent who will not punish bad moves. I recommend you play 9x9 and after 200 games move to 13x13. The best place for ranked 9x9 and 13x13 Go Quest Online which can be played from your phone and has plenty of players of all levels.
The Online Go Server is my favorite English-speaking site. People there are really friendly, and it has a real community feeling. If you speak Chinese (or have the patience to hack your way through a poorly-translated English interface), Fox has a huge userbase and is where top professionals play. If you're looking for something on your phone, I love Go Quest (available on both Android and iPhone), because it's really easy to find games and it has small boards for much quicker games. And finally, if you're looking for an introduction to the game, The Interactive Way to Go is a comprehensive tutorial on the basics that helped me tremendously when I started playing.
For 9x9 GoQuest is a popular app.