As an experienced DQ owner, I pretty much agree with everything Vortex says. The more power the better. I'd say 100 watts (solid state) is the bare, bare minimum. If you're on a tight budget, a good sounding, cheap amp which mates well with DQ's is the Carver TFM-35. "Audiophiles" will scoff, but these are an excellent sounding, high current, low feedback design at 250wpc for around $350 in mint condition on Ebay.
My current DQ20i's are one of the most enjoyable, completely non-fatiguing speakers I have heard - at any price. They are horizontally bi-amped and powered by a CJ Premier 11a on top and a Harmon Kardon Citation 16 on the bottom end.
There are people who have modded their DQ-12's to bi-amp configuration, and you can also easily upgrade the caps in the crossovers and get noticeably improved performance, too.
The one issue I differ from Vortex is on the highs, I have A/B tested these against a number of modern designs and it is clear that the highs are somewhat rolled off (even using solid state amps). I plan on experimenting with incorporating newer tweeters to get just a bit more snap.