Here are all the standard procedures for unclogging nozzles, in order of difficulty/invasiveness.
Nylon Cold Pull
Ultimaker refers to this as the Atomic Method. Warm your hot end up to nylon printing temperature (at least 245°C; 260° if you have an all metal hot end). Push the nylon filament in as far as it will go, then cool off the hot end to 140°C. Yank the filament out. The idea is that the nylon will have stuck to whatever else is in the nozzle, and will pull it out with it. Repeat until the nylon comes out clean. This is a good technique to use on nozzles that are starting to show signs of obstruction, but are not completely clogged yet.
Acupuncture needles, piano wire, or any other thin rigid wire can be inserted into the nozzle hole to push out any obstruction. Obviously, you will need to get one smaller than your nozzle diameter (typically 0.4 mm). This is good for clogs in the very narrowest part.
The following techniques require the nozzle to be removed from the hot end. At this point, you should make sure that the blockage is not higher up in the hot end as well. With the nozzle removed, warm up the hot end and push some filament through by hand. This will make sure that the barrel and heat break are clear. When you put your nozzle back on, remember to bring the hot end up to temp before tightening it.
This is only for ABS, since it dissolves in acetone. Remove the nozzle and let it soak overnight.
With a MAPP gas torch, it only takes a second or two to melt any plastic in the nozzle. A few more seconds will incinerate whatever is left. Be careful. Some hot ends (like the Budaschnozzle) have aluminium nozzles. Heating these for very long with cause the metal to soften.