The following problems are cherry-picked from the large selection of problems. By no means limit yourself to this list - these are just to get you started!
|A Plus B||Warmup||Link|
|Snakes and Ladders||Implementation||Link|
|Smiles with Similes||Implementation||Link|
|Federal Voting Age||Simple Math||Link|
|Moore's Law||Simple Math||Link|
|Tin Can Telephone||Intermediate Math||Link|
|Friends||Simple Graph Theory||Link|
|Jelly||Simple Graph Theory||Link|
|Shop and Ship||Intermediate Graph Theory||Link|
|Trucking Troubles||Intermediate Graph Theory||Link|
|Convex Hull||Intermediate Graph Theory||Link|
|Pi Day||Simple DP||Link|
|Bowling for Numbers||Simple DP||Link|
|Origin of Life||Intermediate DP||Link|
|Nutrient Tree||Advanced DP||Link|
|Greedy for Pies||Advanced DP||Link|
USACO is equivalent to CCC (designed for high-school students), and has an online training curriculum.
CodeForces is an online contest platform with regular contests, including some sponsored by companies.
TopCoder is another popular contest platform, and includes ratings like DMOJ and CodeForces.
The sphere online judge has a wide collection of problems and contests to choose from.
CodeChef allows for longer duration competitions that are ideal for beginners.