Do electrolytic capacitors have a limited shelf life?
Aluminium Electrolytic Capacitors:

Epcos:
2 years, cf. this applications information

Cornell Dubilier:
3 years as per this document

Nichicon:
2 years; section 2-6 in this document

Several documents say that longer storage is well possible, but will require reforming before use. Panasonic, amongst others, has a number: Apply the rated voltage via a series resistor of 1 kOhm for 30 minutes (for example http://www.panasonic.com/industrial/components/pdf/aluminum_app_dne.pdf). There is also a military handbook about reforming stored electrolytic capacitors (formerly known as MIL-STD-1131).

Without reforming and by applying the rated voltage after a long storage duration, the reforming current might be so high that capacitors may get (too) warm and even blow up, which we do not like because we are not Beavis or Butt-Head (he he).

Tantalum Capacitors:

I couldn't find similar data after my initial search, but it seems like the usual MSL (moisture sensitivity levels) ratings for surface-mount parts are given and applicable.