Self-Discharge. Normal NiMH's have the highest self-discharge rate of any kind of battery (meaning they lose charge just by sitting around, unused), but there are Low Self-Discharge (LSD) versions available (like Sanyo eneloop). The tradeoff is that the LSD versions have a little lower capacity. So when buying NiMH's, you have to choose between longer shelf life or higher capacity. If you burn through batteries quickly, get the regular NiMH's so you can enjoy the larger capacity. But if you go months before using up the battery's capacity, go for LSD instead. The table at right shows the relationship between self-discharge and capacity.
One nice thing about the LSD versions is that they come pre-charged. Regular NiMH's must be charged before use.
Voltage. NiMH's are rated at 1.2V initial voltage, which is lower than the 1.5V that alkalines put out at first. This is generally not a problem, but it does mean that flashlights will be dimmer at first, and devices that need 4 or more batteries might burn through the batteries very quickly or not work at all. On the other hand, some devices (like many digital cameras) are designed to work with the lower 1.2V, so the reduced voltage is definitely not a problem there. If NiMH's don't supply enough voltage for your device, consider NiZn's, or mixing NiMH and NiZn together, after seeing the caution about mixing NiMH and NiZn in the same device.