As long as the parameters of a new capacitor are correct then you can probably substitute it in place of the original one.
The main things to consider when selecting a new capacitor are.
- Rated voltage
- Allowed ripple current
- Rated temperature
Ideally find a capacitor where all the above factors are as close as possible to the original. If you can't find a capacitor with identical parameters follow the guidelines below.
Rated voltage: Try and make this identical to the original, but higher rating is usually OK. If using a lower voltage rating the part may fail.
Capacitance: Try and match to the original value. But ±20% would probably be OK for most stuff considering aluminum caps tend to have ±20% tolerance anyways. For bulk power supply decoupling, using a higher value (within reason) is also probably OK.
ESR: Try and get somewhere close to the original. A little more or less is probably OK. Going for a lower value could improve power supply efficiency and noise, but it could also destabilize the supply if the ESR was being used for damping/stability.
Allowed ripple current: Any value greter than or equal to the original is OK.
Rated temperature: The maximum rated temperature should be at least as high as the original part. For the lowest rated temperature you need to match the operating conditions of the device. If you don't plan to operate the device in freezing temperatures, then you probably don't need a minimum rating below 0C.
Note that capacitor lifetime decreases exponentially with operating temperature. If you can find a capacitor with a higher maximum rating than the original, it can dramatically increase the operating life of the part.