I'm currently an undergraduate and have a cGPA of about 3.6 in Mathematics. I worry that it's not good enough to land me a place at some of the best graduate schools such as UCB, Princeton and MIT. I still have a little over a year left till I get my degree, which means that I still have time to mess up or increase my GPA. So I guess my question is pretty straightforward, is my GPA enough? What more should I do to improve my chances? I've loved mathematics since a long while but now I fear that I'm worried only about maintaining good grades which has made me lose interest in everything I study. I want to get the same interest that I had back but the grades keep holding me back from it. I initially wanted to delve into research but given that I've lost interest in everything how can I expect it to be fun?What do I do to fix that? Any help would be appreciated.
The 3.6 looks a bit weak, but there's lots of other relevant information that's not in your question. For example, a poor grade in first-year calculus wouldn't matter so much if you have solid A's in more advanced courses; on the other hand, solid A's in calculus followed by lower grades in more advanced and theoretical classes would be a serious problem. Also, letters of recommendation are very important in graduate admissions. If you've done a research project and your supervisor writes an ecstatic letter about the quality of your work, that can compensate for lower grades in some classes.
You may consider that (i) everyone wants to get into these departments, but not everyone can (even among those who have a perfect GPA), (ii) the U of TX, U of CO, U of MI group of universities ain't bad either.
In the end, your GPA is only one aspect of the puzzle. An important part is also where you get your undergraduate degree. A GPA of 3.6 doesn't count nearly as much if you're at Pomona City College or Fresno State, than if you are at MIT or a highly selective liberal arts college. That is, unfortunately, not something you can do anything about at this point in time, but it's worth keeping in mind when you wonder what you aspire to.
Ultimately, while I applaud you for aspiring to go to MIT, UCB, etc, you will find that in the long run it's unhealthy to expect to get there. Very few people do, but most come to realize that being on the next step down is not a bad place to be either. Setting achievable and realistic goals is a worthwhile endeavor.