Added note: You can do a VERY rudimentary test of a cap with a multimeter in continuity mode. Hooking the cap up to the multimeter should show up as an open circuit (infinite ohms, or needle at original position on the left side). It is possible with large capacitors for it to take several seconds for the reading to settle back down to infinite ohms.
This test is only conclusive if the cap reads less than infinite ohms for a very long time, this indicates a short circuit in the cap. But no other situation can be detected this way. (i.e. leaked and dried out caps still test as open circuits)
It is very possible for a capacitor to have degraded and now has a different actual capacitance than it used to have, but still functions like a capacitor, just the wrong size now. It either requires a calculated circuit and oscilloscope or some dedicated equipment to test the actual capacitance (in Farads, usually µF, nF, pF range). Even with this, bad capacitors may test good because they may function fine at low voltages used for testing but fail at the higher voltages present in the actual circuit board they came from.
In short, capacitors are CHEAP, and it's usually a much better use of time to just replace them instead of bothering with testing.