Tuples aren't currently all that large a benefit in C#, because there isn't any neat syntax for them. However, the concept is very common in functional languages such as F# (new to .NET 4.0).
So, if you're writing part of your application in F# or if you're using libraries written in F#, you might run into them. If you're using only C#, I'd say you're better off using anonymous types. They allow you to name the various properties, whereas they will be called Item1
through ItemX
using tuples. Not very descriptive.
Of course, if you want to return multiple values (with different types) from a method, using anonymous types isn't an option, in which case using tuples might be a decent solution if you're making something quick and dirty.