Settle up your lawsuit. This is the best way to stop process servers because it also removes your obligation to appear in court. So, if you owe money to someone and are being sued, the best way to stop the process server is to pay your creditor back.
Change your routines. The process server cannot serve you unless he finds you and positively identifies you. If you change your routines enough then he will not be able to find you and may eventually give up.
Tell your family members not to accept papers on your behalf. If a process server cannot find you then she can just give your papers to a relative if the relative agrees to take your papers on your behalf.
Be vigilant. If a stranger asks you your name you are under no obligation to tell him what it is. If you are trying to stop a process server, you need to make sure he cannot identify you.