Electronic Design has a smart battery charger schematic using only a single transistor. This is interesting as similar circuits now contain simple integrated circuits. When the battery’s charge falls below a threshold voltage, it is automatically recharged to a preset voltage. Unfortunately, the circuit has a couple of major flaws.

1. The single silicon junction makes the circuit extremely sensitive to ambient temperature changes. In the comments, someone mentions 0.5V per 10° which sounds about right.
2. When the power supply is disconnected (through power outage or physical disconnection), the battery discharges through the resistors.

For portable devices, you can avoid the second flaw by building the circuit into an external charger. However, this is not possible with UPS’s or other homemade backup power supplies.