You want to do everything possible to make your characters memorable and compelling to readers and audiences, so why cram your narrative worlds with Johns and Susans?
Of course, you can go too far with this. I remember seeing a Julianne Moore movie in which her name was Telly.
Telly? Isn't that a muppet?
A device I often use is to take some key aspect of the character or their place in the story and let that suggest the name. Hell, any trick that's good enough for Dickens, the Restoration dramatists, and the makers of Max Payne is good enough for me.
Some examples from my scripts:
(Caveat: No disparagement meant for people who have these names but not these characteristics!)
Val, short for Valerie. Horror heroine. Valiant, valkyrie.
Bridget. A two-fer, since this character is inflexible (rigid, stringent) and sexually cold (frigid).
Lance. Easygoing guy, loose where Bridget is not. Also a little dreamy, not very grounded in real life.
Fay. Seductive world traveler. More dangerous than she first appears, like faerie, Morgan Le Fay.
Roger. A scoundrelly, womanizing Englishman. A play on the British slang meaning of the word.
Galen. A twist on Gawain, the knight. The character is honorable, noble, and plays fantasy games.
Neva. A similar twist on Guenevere.
Abigail. Buttoned-up, prim, religious.
Reyna. Powerful CEO. Reign, and reine is French for queen.
Clayton. A man of substance, figuratively and literally, but also weak, feet of clay.
This works with surnames and full names as well: I named a character Tim Pritchard because that suggested he was a little untrustworthy and kind of a dick, which he was. And Palmer Sykes just sounds like a child molester, doesn't he?
Many BATTLESTAR GALACTICA characters have a regular-sounding name spiced with something more fantastical, often pulled from ancient history or mythology. Karl Agathon, Kara Thrace, Sharon Valerii, Gaius Baltar. A neat way to suggest sci fi without all those damn apostrophes that apparently we'll all be using in the future. Qapla'!
And for horror stories or thrillers, I'm reminded of the Bill Cosby routine where you should name your kid something that yells well down the block, that is, doesn't end in a consonant. Compare the bellowing-into-the-haunted-basement possibilities of "FRANK!" and "BILLYYYYYYYYYYYYYYYYY!"
What are your own methods for naming?