Handling and storing elapsed time
TimeSpan has an Int64 Ticks property that you can store instead, and a constructor that takes a Ticks value.
I think the simplest is to just convert user input into a integer number of seconds. So 54:12 == 3252 seconds, so store the 3252 in your database or wherever. Then when you need to display it to the user, you can convert it back again.
For periods less than a day, just use seconds as other have said.
For longer periods, it depends on your db engine. If SQL Server, prior to version 2008 you want a datetime. It's okay- you can just ignore the default 1/1/1900 date they'll all have. If you are fortunate enough to have sql server 2008, then there are separate Date and Time datatypes you can use. The advantage with using a real datetime/time type is the use of the DateDiff function for comparing durations.