ReSharper likes to point out multiple functions per ASP.NET page that could be made static. Does it help me if I do make them static? Should I make them static and move them to a utility class?
Static methods versus Instance methods
Static and instance members of the C# Language Specification explains the difference. Generally, static methods can provide a very small performance enhancement over instance methods, but only in somewhat extreme situations (see this answer for some more details on that).
Rule CA1822 in FxCop or Code Analysis states:
"After [marking members as static], the compiler will emit non-virtual call sites to these members which will prevent a check at runtime for each call that ensures the current object pointer is non-null. This can result in a measurable performance gain for performance-sensitive code. In some cases, the failure to access the current object instance represents a correctness issue."
Utility Class
You shouldn't move them to a utility class unless it makes sense in your design. If the static method relates to a particular type, like a ToRadians(double degrees) method relates to a class representing angles, it makes sense for that method to exist as a static member of that type (note, this is a convoluted example for the purposes of demonstration).