Method can be made static, but should it?

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.)

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).

Marking a method as static within a class makes it obvious that it doesn't use any instance members, which can be helpful to know when skimming through the code.

You don't necessarily have to move it to another class unless it's meant to be shared by another class that's just as closely associated, concept-wise.

I'm sure this isn't happening in your case, but one "bad smell" I've seen in some code I've had to suffer through maintaining used a heck of a lot of static methods.

Unfortunately, they were static methods that assumed a particular application state. (why sure, we'll only have one user per application! Why not have the User class keep track of that in static variables?) They were glorified ways of accessing global variables. They also had static constructors (!), which are almost always a bad idea. (I know there are a couple of reasonable exceptions).

However, static methods are quite useful when they factor out domain-logic that doesn't actually depend on the state of an instance of the object. They can make your code a lot more readable.

Just be sure you're putting them in the right place. Are the static methods intrusively manipulating the internal state of other objects? Can a good case be made that their behavior belongs to one of those classes instead? If you're not separating concerns properly, you may be in for headaches later.

You should do what is most readable and intuitive in a given scenario.

The performance argument is not a good one except in the most extreme situations as the only thing that is actually happening is that one extra parameter (this) is getting pushed onto the stack for instance methods.

I hope you have already understood the difference between static and instance methods. Also, there can be a long answer and a short one. Long answers are already provided by others.

My short answer: Yes, you can convert them to static methods as ReSharper suggests. There is no harm in doing so. Rather, by making the method static, you are actually guarding the method so that you do not unnecessarily slip any instance members into that method. In that way, you can achieve an OOP principle "Minimize the accessibility of classes and members".

When ReSharper is suggesting that an instance method can be converted to a static one, it is actually telling you, "Why the .. this method is sitting in this class but it is not actually using any of its states?" So, it gives you food for thought. Then, it is you who can realize the need for moving that method to a static utility class or not. According to the SOLID principles, a class should have only one core responsibility. So, you can do a better cleanup of your classes in that way. Sometimes, you do need some helper methods even in your instance class. If that is the case, you may keep them within a #region helper.

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();

It helps to control namespace pollution.