Pay attention to the ages of your characters and what period it is set in. Have you ever noticed that you can hazard a good guess about the age of the deceased (if you read obituaries, which I confess that I do) by the name? Names come in waves and fads. Cemeteries are good places to find names that are supposed to be from 50-100 years ago. If your characters are supposed to be about your age, and contemporary with our world, try first names that you remember from elementary school. Last names change less, but try for a good mix of ethnic types when appropriate.

I've been known to use various combinations of patients' names (true confession time), or other real people that I know.

Fantasy names are tougher. I recommend using real Earth languages rather than made-up language. I'd rather see transplanted Celtic names in a castles-and-dragons fantasy than something that feels artificial.