Unless you have just arrived from the other side of the galaxy (where such problems do not exist), you know that so-called 'leak-proof' batteries (even those with fancy warranties and high budget advertising) sometimes leak. This is a lot less common with modern technologies than with the carbon-zinc cells of the good old days, but still can happen. It is always good advice to remove batteries from equipment when not being used for an extended period of time. Dead batteries also seem to be more prone to leakage than fresh ones (in some cases because the casing material is depleted in the chemical reaction which generates electricity and thus gets thinner or develops actual holes).
In most cases, the actual stuff that leaks from a battery is not 'battery acid' but rather some other chemical. For example, alkaline batteries are so called because their electrolyte is an alkaline material - just the opposite in reactivity from an acid. Usually it is not particularly reactive (but isn't something you would want to eat). One exception is the lead-acid type where the liquid inside is sulfuric acid of varying degrees of strength depending on charge. This is nasty and should be neutralized with an alkaline material like baking soda before being cleaned up. Fortunately, these sealed lead-acid battery packs rarely leak (though I did find one with a scary looking bulging case, probably due to overcharging - got rid of that in a hurry). Nickel Cadmium cells contain so-called heavy metal compounds which are also bad for you if you feast on them but can be safely cleaned up without harm. Scrape dried up battery juice from the battery compartment and contacts with a plastic or wooden stick and/or wipe any liquid up first with a dry paper towel. Then use a damp paper towel to pick up as much residue as possible. Dispose of the dirty towels promptly. If the contacts are corroded, use fine sandpaper or a small file to remove the corrosion and brighten the metal. Do not use an emery board, emery paper, or steel wool as any of these will leave conductive particles behind which will be difficult to remove. If the contacts are eaten through entirely, you will have to improvise alternative contacts or obtain replacements. Sometimes the corrosion extends to the solder and circuit board traces as well and some additional repairs may be needed - possible requiring disassembly to gain access to the wiring. Don't forget that many batteries do come with explicit or implicit warranties against leakage (and resulting damage) which cover the equipment they are in as well. Thus, you may be able to obtain a replacement device from the battery manufacturer for at most shipping charges. I don't know if this extends to expensive products like palmtop computers :-).
