David Smith's response is correct: just about ANY cell CAN leak, and probably will, given time. Careful manufacture can minimize the tendency, of course. But consumer cells just aren't so high-tech as to be totally leak-proof.
A separate but equally important issue is not leaking, per se, but Venting. Rechargeables in particular can do that, and that leads to battery compartment problems as well.
In FACT, if you look at a NiCd or NiMH rechargeable cell. (say a AA size) you will sometimes see the HOLES, usually at the positive terminal cap. All cylindrical rechargeables have holes; some are visible and some are just hidden by the label area. These are to vent off a gas buildup in the electrolyte that occurs while charging, and especially if overcharging. As a battery "ages", its electrolyte is more likely to dry out and this outgassing increases. So terminal corrosion in the form of "hazing" is very common, and gold plating is recommended in applications where outgassing is possible.
Since gold is expensive, most manufacturers use a "corrosion-resistant" bright-metal alloy instead. It looks a lot like gold, but can still haze up pretty badly. When "hazed", they are not as good at conducting, and so you want to keep them shiny. Polish these contacts with #2 plastic polish and a small felt wheel or vigorous q-tip.
In a LEAK situation, real corrosion of the metal results, even on gold, and you will lose metal... so it is important to clean up a leak immediately and thoroughly. Towel and q-tip and cotton-ball clean every bit of electrolyte; follow up with isopropyl alcohol wipes. When your battery compartment is clean and dry, any corroded spots on the metal contacts or springs need to be scrubbed (an old dry toothbrush works well).
Inspect the metal; green or blackened areas need to be worked on further. Very very fine (000?) steel-wool of the sort used by furniture refinishers can clean contacts very well, BUT in doing so realize that the sheddings of this stuff are a danger to circuitry, so shield your calculator well prior to working on it this way.
Do button-cells leak? Sometimes, yes. More likely, you've seen a button cell swell (take on a convexity). If they do so, replace them IMMEDIATELY *no matter if they still work*.
Zinc-air cells leak notoriously. They need those holes to activate; but those holes are an achilles heel. I do not recommend zinc-air cells in any calculator application anyway; but they've found their way into pagers and the like and are the de facto standard in hearing-aids. If you use zinc-air in a calc, take them out if you won't be using the calculator for more than a week.
Much speculation about making "pseudo" batteries run by AC to power your displayed calcs... hmm, simpler to me is to SEPARATE battery from calc with a length of WIRE. Attach wires to contacts on calc, attach to a battery pack of proper voltage SOMEWHERE ELSE, and you'll never, never have calc damage. Even AC adapters and charging circuits will be properly fooled if you do this right.
