I think the others have mentioned the times when you should and shouldn't perform "safe casting" (where you ensure that the cast can succeed before risking an exception). If your program does need to perform safe casting then the TryCast method saves both you and the program some work.
I wasn't aware of the TryCast() function until today, and I feel like a fool for using the 'bad' method of safely casting.
If you did not know about the TryCast() function then you might end up with something like this:
'' wasteful, the TypeOf and DirectCast calls are redundant
If TypeOf obj Is SomeClass Then
someObj = DirectCast(obj, SomeClass)
'' More code
End If
The problem is that this method actually performs two casts (technically I think they're actually type-checks). Using the TryCast and checking if the result is Nothing eliminates the 2nd cast and saves needless work.
'' efficient, only one cast is ever performed and there are no InvalidCastExceptions thrown
someObj = TryCast(obj, SomeClass)
If someObj IsNot Nothing Then
'' More code
End If
Following this pattern lets you avoid having to handle expensive exceptions, and efficiently cast to the correct type.