cyccommute 

Probably. Shift to the lowest tension which is usually the highest gear (smallest cog on the back). Check the tension on the cable by plucking it. It should have a little bit of twang but it shouldn’t be as tight as a guitar string. Most of the time the cable is too slack...indicated by being able to pull it away from the frame...but sometimes it is too tight. If it is “twangy”, back off on the barrel adjuster on the rear derailer or on the shifter or frame (depending on what kind of shifter you have). Then run the bike through the gears. One click should move the derailer on gear.

If that doesn’t work, you might have some issues with the outer cable. It might be dragging on the inner cable causing too much tension. Shift the bike to the lowest gear (largest cog, again assuming regular “high normal” derailer). (The pictures below are for a mountain bike but works for road bikes too)

Library - 3391 by Stuart Black, on Flickr

Now, without pedaling, shift up which releases tension on the cable

Library - 3392 by Stuart Black, on Flickr

This will make the cable very slack

Library - 3393 by Stuart Black, on Flickr

You should be able to pull the cable out of the frame

Library - 3394 by Stuart Black, on Flickr
Library - 3395 by Stuart Black, on Flickr

and pull it away from the shifter as well. Put a little grease on your thumb and forefinger and run it up and down the inner cable. Lubricate anything that is under the outer cable.

While you have the cable slack, inspect the ends of the cable and see if there are any wires poking out of the ferrule like this

IMG_1361 by Stuart Black, on Flickr

If there are, this means that the outer cable probably needs replaced since the rods in the outer cable have come loose. The loose wires will cause the inner cable to jam. You should be able to pull most ferrules off the cable housing to look for this kind of stucture

IMG_1362 by Stuart Black, on Flickr

Cable tension and cable lubrication are usually the problem. That should cover 99% of all issues. If that doesn’t work, check the derailer hanger...you can eyeball it to see if the cassette, upper wheel and lower wheel line up. But it’s usually the cable.