Thing that motivates me most is competition. Social element, so stream and friends you can add and then check up on, is great and I love it. But: all my friends now stopped doing exercises daily and I'm starting to lack the urge to get going. I surpassed them all and now there's no one to compete with. So my idea is implement that feature on higher level and do the general learners' ranking. Everyone would be assigned a position that reflects total points they've got. Doing some lessons and then checking raised position in ranking would be a wonderful motivation to continue learning. Also it could be only Spanish ranking, monthly, weekly and daily ranking, sentences translated ranking, timed practice completion time ranking and so on. Sky is the limit. Timed practice is a great feature, but it still could be extended though. Real-time compete with others, additional points for time left and why should we and at 20? Please consider adding such functionality to get us all going. I love how is Duolingo getting better recently. Keep up the good work!
I strongly agree with you, gamifying the system even more would be great. I do believe that doing this is going to encourage people more and more to use the website and share with others. I mean, the site has it's own intrinsic motivation that is: "I want to learn a language", if you really fill it with extrinsic motivators you might ruin the experience for those that just want to learn the language but you can't deny that competition is a pretty good motivator!
Right now a lot of space at home page is taken by leaderboard list. It could be adjusted by adding a drop-down list to choose other lists-rankings (general, weekly, etc.), so choosing more competition would be optional.