I would like to just add a point of interest to this thread. Many many threads have dealt with this issue and have all said pretty much what "hansbert" stated. BUT I would like to throw out the following incidents that have happened to myself and to at least 3 other Americans that I know from Puerto Plata.
AFTER the 911 attack, immigration has been a little more strict on their duties at least in POP. I have been going back and forth almost on a or bimonthly basis for the last 9 years. (Within the last 2 months I got my permanent residency so it doesn't matter now), but we each have US passports with multiple entries to the DR. We are not related and only live in the area of Puerto Plata and see each other at the airport on occasions. Well, I was one time, along with them according to their accounts., pulled aside at the second stop where they normally take the copy of your tourist card after the immigration booth, and they took my passport and for 1/2 hour went in the back room with it. When they came out, it appeared to have check marks on many of the entry and exit stamps as if they were checking to see if I came in and went out on a regular basis without overstaying. The passport was then given back to me and I have never had a problem since. JUST THOUGHT IT MIGHT BE A THING TO THINK ABOUT.