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
For complex logic within a class, I have found private static methods useful in creating isolated logic, in which the instance inputs are clearly defined in the method signature and no instance side-effects can occur. All outputs must be via return value or out/ref parameters. Breaking down complex logic into side-effect-free code blocks can improve the code's readability and the development team's confidence in it.
On the other hand it can lead to a class polluted by a proliferation of utility methods. As usual, logical naming, documentation, and consistent application of team coding conventions can alleviate this.
It helps to control namespace pollution.
If the functions are shared across many pages, you could also put them in a base page class, and then have all asp.net pages using that functionality inherit from it (and the functions could still be static as well).
Making a method static means you can call the method from outside the class without first creating an instance of that class. This is helpful when working with third-party vendor objects or add-ons. Imagine if you had to first create a Console object "con" before calling con.Writeline();
Just to add to @Jason True's answer, it is important to realise that just putting 'static' on a method doesn't guarantee that the method will be 'pure'. It will be stateless with regard to the class in which it is declared, but it may well access other 'static' objects which have state (application configuration etc.), this may not always be a bad thing, but one of the reasons that I personally tend to prefer static methods when I can is that if they are pure, you can test and reason about them in isolation, without having to worry about the surrounding state.
Performance, namespace pollution etc are all secondary in my view. Ask yourself what is logical. Is the method logically operating on an instance of the type, or is it related to the type itself? If it's the latter, make it a static method. Only move it into a utility class if it's related to a type which isn't under your control.
Sometimes there are methods which logically act on an instance but don't happen to use any of the instance's state yet. For instance, if you were building a file system and you'd got the concept of a directory, but you hadn't implemented it yet, you could write a property returning the kind of the file system object, and it would always be just "file" - but it's logically related to the instance, and so should be an instance method. This is also important if you want to make the method virtual - your particular implementation may need no state, but derived classes might. (For instance, asking a collection whether or not it's read-only - you may not have implemented a read-only form of that collection yet, but it's clearly a property of the collection itself, not the type.)