Add solutions to problems at http://rosettacode.org. Even if your solution is suboptimal, someone is likely to come along and improve it. Or create a totally new problem and solve it in your language of choice.
I can recommend Rosalind http://rosalind.info/problems/locations/
It has bioinformatics problems. They start really easy ("count the bases in a DNA sequence") and get progressively harder.
For each problem you get some sample data to work with. When you think you've figured it out, you can download a dataset to run your algorithm against, then upload the output to see if you are correct. There's a time limit for submission, and although you can keep re-trying, the data sets are different each time.
Check it out! Don't let the bioinformatics part throw you off.
I highly recommend the book "Programming Challenges" by Steven Skiena, used in conjunction with UVA Online Judge at http://onlinejudge.org.
Each challenge takes the form of a word problem. The solution can be coded in a few different languages and uploaded to the website.
The site imposes time limits when running the solution. When I've found that my solution works but is too slow, it has encouraged me to look for different data structures or algorithms.
I can't recommend it enough.
Have you tried www.hackerrank.com ? I have not personally used it. Also, I am not a big fan of algorithmic problems either.
Someone on HN posted the Martyr2's mega project list: https://github.com/thekarangoel/Projects
You could take some inspiration from it.
Both codechef and SPOJ are good enough , focusing on one will be a good strategy. You may give a try to interviewstreet as well. But like I said mastering problems on any one of the sites is sufficient .
You can only brute force the first handful of Project Euler problems. You quickly hit problems where the difference between the right and wrong approach is seconds vs hours or days.
The Art of Computer Programming, Knuth.
topcoder.com
Keep going with Project Euler. It's not long before the brute force approach stops working. On later problems you will find many ways to solve them but very few that return an answer in less than a week, say.