There isn't a convention in the same sense as asynchronous operations (BeginXXX EndXXX), however it is used to differentiate between code that will do the same as other code, but does not throw exceptions, either by swallowing exceptions or not generating them.
If your code is an alternative to another method that does not provide exception handling, I would prefix it with Try because it is somewhat recognised - and .NET people will first assume it's behaviour will not throw exceptions.
This can be re-inforced by returning a bool for success and placing the return value as an out parameter.
To answer the question - it shouldn't just be placed around any method that handles exceptions; only in instances where it makes sense logically to offer the behaviour I outlined; the behaviour currently offered by some instances in the .NET Framework.