Nickel based batteries (used in rechargeable AAs and old mobile phones) - yes. If your charger works using a timer and you try to charge some batteries that are already charged, you'll end up overcharging them because the charger won't know they're fully charged. If your charger works by stopping charging automatically when the batteries are full (this feature is common on fast chargers that take only 1 to 5 hours to charge a battery, and is also the kind of charger you find in old mobile phones), then yes you can overcharge batteries slightly if you place fully charged batteries in the charger, because the charger won't immediately know that your batteries are already full; it tries charging them and then realises that the batteries are full when it detects that the batteries are heating up (so the batteries will actually be being overcharged during this period). If you fully charge an old mobile, then let it cool and connect the charger again, the same thing will happen. Severely overcharging a nickel-based battery will make it swell up and eventually explode...
If you're not sure whether your mobile falls under this category, open it up and see whether you can read "Ni-MH" or "Ni-Cd" on the battery. If, on the other hand the battery reads "Li-ion" or "Li-Po" then the mobile falls under the category I describe below:
Lithium based batteries (used in most modern electronic devices like mobile phones, laptops, PDAs and just about everything) have a protection circuit, built into the battery iteslf, that disconnects the battery when the voltage reaches 4.25 volts per cell, so it's pretty impossible to overcharge one of these. However, protection circuits might go wrong (or the battery doesn't have a protection circuit; you'll only find unprotected batteries in high-performance radio controlled cars or planes, if at all), then yes, overcharge is possible, in which case the battery will vent with flames...
Lead acid batteries (used as the big starting battery in your car, and in some cheap small electric cars or golf carts) have a very good tolerance to overcharging... if you overcharge it, you'll only get bubbles forming in the electrolyte (if you've ever seen a car battery "boiling" after a few hours connected to the charger, this is what you're actually seeing). The bubbles aren't caused by the water actually boiling, but decomposing into hydrogen and oxygen gas (electrolysis). It doesn't damage the battery, in fact when you see these bubbles start to form it's a sign that that battery is fully charged.