About all you can do is inspect for signs of leaking, bulging, etc. Good time to clean out dust too. If it looks good, fire it up and see how it works.
The only other consideration is in cases where the device failure could cause damage to much more expensive equipment. Then it's a judgment call whether to try it.
If you want to check deeper, you could use an ESR meter to give a better indication of the electrolytic's condition.
en.wikipedia.org
edit Another thought: Old people working on radio transmitters used to put a variac between the wall plug and the device, and slowly bring up the line voltage (while monitoring current draw). This gives the electrolytics time to reform, and limits the damage if something lets go. It wouldn't work on most modern low voltage devices with switching power supplies.