Q:

Do components have an un-used lifespan?

Lets say for example, that I had a box full of transistors, resistors, capacitors, diodes, leds, this and that, and left it in a cool, average environment for lets say... 50 years.
Do these components have a lifespan while been unused? Do the insides end up degrading and become unusable like cars? Or do they just... Sit there?
I'm asking this, because I just got a thought that struck me, being that if you kept today's components, (and kept them for 50 years) will you be able to use them in the future?

A:

Yes, they will degrade little by little; they will grow tin whiskers, maybe oxidize little by little because their casing will never be 100.00% sealed. Also the pin plating will oxidize, so you'll have to treat them before soldering. Also moisture can creep in, little by little... difficult to say if it would affect discretes like transistors a lot, but ICs will suffer. 
Oxidization plays a role in IC degradation if the passivation layer has defects, but the killer is metal whiskers between pins, pads and bond wires. It doesn't cause gradual degradation; basically the chip works fine until finally a whisker causes a short circuit between pads and the chip dies. 

Image: whiskers on a piece of zinc. Source: http://commons.wikimedia.org/wiki/File:Zinc_whiskers.jpg

A:

Like cars, if kept in an ideal environment (cool and dry) a few things will deteriorate but most will not (at least not very fast). In particular, electrolytic capacitors and batteries will tend to be dead (especially the latter). Rubber will tend to deteriorate (DVD door or cassette drive belts) and speaker cones can also deteriorate (my Keil AMT speakers need re-woofering). Electrolytic capacitors tend to dry out. 
There's plenty of electronics around from 1965, and things have not changed so much in basic technology.. it's generally salvageable but perhaps not fully functional out of the crypt. Something like a UPS that is mostly battery cost-wise is probably scrap for economic reasons, even if 95%+ of the parts are still fine. 
Semiconductors are usually pretty much immune to aging if they're kept cool and not powered. 
The biggest reason why parts have a best-before date is corrosion that makes them difficult to solder reliably. That's not a problem if they're assembled into a product, but if you've got reels of diodes, for example, the diodes may be just fine, but so corroded they cannot be used reliably (at least not without some kind of uneconomical rework). Storing them in low-humidity cabinets and using sulfur-free packaging (brown cardboard boxes are often bad) will help. 

A:

Do these components have a lifespan while been unused? Do the insides end up degrading and become unusable like cars? Or do they just... Sit there?

Sure, this lifespan is called shelf life.
What happens when it passes? Here is an analysis with nice pictures. Here is another one.

