You will not be able to buy an off-the-shelf charger for individual lithium-ion cells, the way you can for NiCd or NiMH rechargeable cells (AA & AAA for example). Lithium-ion requires more protection circuitry that keeps it from being overcharged (allowed to charge to too high a voltage) or overdischarged (too low a voltage) as either of those is very detrimental to the cell chemistry and may destroy its usability in one shot, certainly with repeated abuse, or even cause a fire or explosion. A pack the size of a laptop battery will also have protection against overtemperature, imbalanced cells in a multi-cell arrangement, short circuit, and so on. It may even have an encrypted code to block use of counterfeit (aftermarket) replacement packs. Removing this protection is not necessarily going to make a battery blow up, so long as it's charged and discharged in a safe way, but it will be less safe. You might want to keep it in a ventilated metal box or find some other way to make sure a firecracker-sized explosion won't hurt you if things go wrong.
If you're a hobbyist and want to run a project from a single Li-ion cell, you can do it easily enough by charging the cell on a bench power supply with BOTH current and voltage limit set appropriately for the particular chemistry. As you don't have tech specs for the cells in hand, you'd be wise to be conservative with the voltage and current limit, reducing below what Charith Perera recommended and set it around 3.8V and C/5, or 500mA for a typical laptop cell (cylinder 18mm x 65mm). That will reduce the amount of charge the battery stores, but you'll get many more cycles out of it. You can disconnect the bench supply after it goes into voltage limit mode and the cell will have most of the charge it's going to take at that voltage limit, or you can leave it a few hours more and get a little more charge into it, but don't leave it charging forever.
If you don't have a bench power supply and don't want to build your own charger circuit using standard chips from the likes of Maxim, TI, etc., then no, you probably cannot safely charge lithium-ion cells. Off the shelf chargers (like for a digital camera battery) can be designed differently from one model to another and it'd be harder to characterize their behavior than to build your own. On the other hand if you used a standard digital camera battery to power your project, then obviously it'd be fine to charge it in the associated charger. You'd still want to have a circuit in your project that turns it off when the battery voltage gets below a certain level (say 3.0V to be conservative), as overdischarging the battery will effectively destroy it. You can't discharge a rechargeable battery to zero volts the way you can with a capacitor or a disposable alkaline battery.