What should my heart rate be while running?

Up to 120's, usually: You have not said if you were running for exercise or just running briefly (e.g. To catch a bus). For exercise you are recommended to aim for 85% of (220 minus your age). If your heart rate rises gradually and stays steady, it's likely normal (how fast and to what rate is a function of the shape you're in). If it jumps up & down, it may be an arrhythmia - see a doctor!