There are two fears that a person usually has. First, the fear of the priest judging you. I have been to confession to dozens of different priests all around the country. I have only encountered 1 or 2 that I felt were "judgmental," and in all truth, that was the kind of priest I needed at the time. Sometimes I need the priest to tell me I'm being too hard on myself, but sometimes I need him to tell me I'm being too easy on myself. That being said, if you get a priest who is overly rude or yells at you, there is nothing wrong with leaving and going to a different priest.
The second fear is of a priest breaking the seal of confessional. I think this fear is largely unwarranted. First, priests hear dozens of confessions each week, and most priests forget what they've heard by the time they're finished hearing confessions. Second, your sins are not unique; don't flatter yourself. Furthermore, most priests are very busy and have better things to do than gossip about your confession. Fourth, you probably don't worry about your doctor sharing your medical secrets with anyone and everyone, and yet they keep written records, whereas the priest does not.
Although not all priests have the courage to be martyred like St. John, there are ways to assuage both fears about going to confession. First, go anonymously. Almost every parish has the option to go behind the screen, where the priest cannot see your face. Second, go to a parish that has long lines (experience has taught me that parishes with high Hispanic populations tend to have longer lines). If you don't want to wait long, get there early to be at the front of the line. If you do both of these, not only will the priest not be able to see you (and therefore not know who is confessing and not be able to judge you outside the confessional) but there will be many others confessing which decreases the likelihood that he'll remember your particular confession.
If it has been a long time since your last confession, make a plan to go at the next available time! Remember you can always call your local parish and schedule an appointment. You don't have to wait for the allotted time. Don't delay! That never solves anything!
Links:Fr. Z's 20 tips for making a good confession
Examination of Conscience