A running heart rate monitor meets the requirements of a runner beyond what is normally offered by a general heart rate monitor. If you are a runner, you may need consecutive timers to do interval training, facility to take laps or an external foot pod to do speed and distance measurements.
Below is a compiled list of running heart rate monitors that have been featured on this web site. It is not an exhaustive list.
This shortened list is merely intended to provide the starting point of your investigation, especially if you are short of time. You should not rule out other monitors not on this list as they may well have other features that you will find very useful.
The most advanced running HRM is the Polar RS800SD system which not only allows you to measure speed and distance, but also cadence and stride length. This information, together with the Polar ProTrainer 5 software, gives you all the tools to plan, execute and analyse your training runs.
If you are a beginning/intermediate runner who does not require the most sophisticated running computer there is, but you still want to measure speed and distance, then I think that the Polar RS200SD is your best bet. It strikes the balance between price and functionality and has excellent user reviews on Amazon. The Sigma Sport PC 15 (no S/D measurements however) and Nike CV10 are good alternatives.