Although nothing to do with microcontrollers per se, there are a couple of MCU boards which can be powered by LiPoly/LiIon cells. Some boards have their own charging circuit, but there are a couple which have not.
Even though this is one of the smallest & cheapest chargers on the market, I know that Sparkfun has some very nice and small chargers as well.
Charging is performed in three stages: first a preconditioning charge, then a constant-current fast charge and finally a constant-voltage trickle charge to keep the battery topped-up. The charge current is 100mA by default, so it will work with any size battery and USB port. If you want you can easily change it over to 500mA mode by soldering closed the jumper on the back, for when you'll only be charging batteries with 500mAh size or larger.
The MicroLipo charger can get hot during charging!
Grab it by the sides and unplug, then let cool before removing the battery - take care not to touch the components during charging!
By default batteries will be charged with 100mA charge current. This can be adjusted to 500mA by soldering a jumper on the underside: