To expand on what foosnazzy said, .NET 3.5 (SP1) is just .NET 2.0 SP2 with some new assemblies. The only reason not to install it on the web site would be if the web site would not run with .NET 2.0 SP2.
This is very different from the way it used to be - installing .NET 1.1 on a .NET 1.0 web site I was responsible for broke the web site, even though the web site wasn't using 1.1 - I had installed 1.1 so I could use a particular tool. The upgrade from .NET 1.1 to .NET 2.0 was an even worse nightmare.
But Microsoft learned from this. .NET versions from 2.0 .NET 3.5 SP1 all use the .NET 2.0 Common Language Runtime (CLR). In fact, people who have installed 3.5 are often surprised to look at the IIS settings and see that their web sites still show as running .NET 2.0. But it's the exact same .NET 2.0, just with two service packs applied. Any site that doesn't use the new assemblies can't be affected at all (beyond what a service pack might do).
To further reiterate what has been said - the C# 3.0 features are independant of the Framework. For instance, you can use anonymous types and lambdas in pure .NET 2.0 code. What you can't do is use LINQ, since that requires the new assemblies in .NET 3.5.