That's completely normal & don't worry too much about it. :) You'll get to know the difference between "normal" pregnancy cramps & cramps that you need to pay closer attention to. Bottom line is you will be increasingly uncomfortable until the little one is born but if it's really bothering you, keep a log of the times it happens & where you feel the cramping and tell your doctor about it at your next prenatal visit.
Chances are you will be told not to worry about it. Unfortunately paranoia about a possible problem during your pregnancy is something most women experience. Try to relax & enjoy it. It's a totally unique experience. :)
Yes cramping is very common during early pregnancy...especially with the first one. As long as your are not not seeing any blood, you should be ok.