Aruba has consistently mild temperatures with no major rainy season. It's a hop-on-to-a-plane-right-now place. Any time at all.
From December through April are touristy months with the weather at its driest. January is a peak visiting month, though if you want to be a part of some festivities, then the last 2 weeks of February are a maelstorm of parties and parades with the Carnival in full swing.
For a more relaxed time, try mid-april to september.
Following Easter, the rates will drop and go down still further in June-November which is the hurricane. That's a good time for a string-budget traveler especially considering that Aruba lies well outside the hurricane belt.
Besides the Carnival in February, you might want to look out for the Aruba Music festival in October and ostensibly the best catamaran sailing event in the world, The Aruba Heineken Catamaran Regatta for a week in November. If you're not sailing, then grab a patch of sand and watch the races. There are other events orgaized for the entertainment of non-sailors too.
Aruba is a brilliant escape plan. In fact I have a friend who's constantly on the lookout for a small island where we're to build our huts and start life anew and I think I just might help him out by suggesting Aruba.
Picture Courtesy: www.flickr.com

A brand new modern apartment complex in Oranjestad. Offers rooms, suites, villa's & apartments.
Very cosy...
Located just between down town & the popular beaches.
On the corner is a bus stop, a supermarket, pharmacy 7 a restautant.
Just try it!