VC&G Collecting Tip: Remove your old computer clock batteries.
I'm serious: do it. Despite my regular battery purges (done to avoid just such a situation), I forgot to remove the Mac IIsi PRAM battery you see above because the computer was buried under a bunch of stuff. The battery electrolyte leaked out and corroded everything it touched, ruining the logic board. Sometimes you can recover from battery leaks with extensive cleaning if the damage isn't that bad. In this case, it wasn't worth the effort. Bye, bye, IIsi.
While you're ditching the vintage clock batteries, do yourself a favor and remove the main power batteries from any laptops in your collection. I typically store laptop batteries in a gallon zipper bag each. Even if the batteries are dead/bad (which they usually are), I save the plastic cases for re-use if I plan to rebuild the battery in the future.
As a good rule of thumb, never keep batteries (no matter how new) in any electronic device for longer than a couple weeks of non-use. Any longer, and you're just playing Russian roulette with your gadgets.
Almost all batteries leak eventually. If your old ones haven't leaked already, you're very lucky. Focus on alkaline and NiCd batteries first, because they leak the worst; lithium cells can leak as well (as seen above), but it's less common overall.
Regardless of the type, if they're old, remove them now — even if it requires clipping or desoldering — and spare yourself the leaky battery blues later on.