Could possibly be fret buzz. What kind of guitar and have you had it set up lately?

Try pressing one string at a time in the correct position (to eliminate chording issues) and pick the string normaly like you would when you play. If any strings still buzz, then you probably need a bit of set up.

If you do have fret buzz, don't panic. Guitars need to be set up sometimes and is not an indicator that anything is badly [u]wrong[/u] with your guitar. Many people get set ups done seasonally like a car.

Guitar measurements are in the thousandth's of an inch, so it only takes a very small misadjustment to start giving you grief. Take it to your local store and they will probably give you a set up for around $50. If you are handy, start researching, and you can save some money.

Good luck!