It really is going to depend on how much you like Aruba. Admittedly not everyone falls in love with the place as much as some of us others do ....too windy, not tropical enough, not lush enough...the list could go on, but I will instead list the positive like great beaches, friendly people, fantastic restaurants, perfect weather...
So a week has ALWAYS has been for me way too short! We only have to fly from Atlanta and I think 4 hours each way on an airplane itself is a big enough feat to warrant spending more time at the destination. One week there and subtract the day you travel in. You eat dinner and then sleep in your hotel room. On the day that you leave Aruba, you eat breakfast and then maybe it is a quick hop in the ocean before checkout and another day lost. So that leaves you with 5 or 6 carefree days, depending on whether you are going for 6 or 7 nights.
For us, 7 days/8 nights last year in Aruba, went by in the blink of any eye. 1 day touring, 1 day on a sailing excursion left us with only 5 days on the beach which is what we love to do best. We've been to Aruba for as long as 15 nights and began to get a little tired of "living" in a hotel and eating dinner out each night. Besides missing our pets, yeah, I could have probably stayed the rest of my life....
12 nights for us is perfect. 10 days to do as little or as much as we want. We'll break up our beach days in the middle of our trip with 3 days of wandering the island: natural pool...butterfly farm...donkey sanctuary...maybe a stop at the Ostrich farm...a day of snorkeling stops around the island...THEN it is back to the beach! 
If you love the beach, you could spend forever in Aruba, or at least until the money runs out. 
