http://www.vidadancefusionfitness.com/zumba.php
Found this info at the link above:
Q: What should I wear?
A: Wear comfortable clothes that you can move in (workout clothes). Because you will be twisting, pivoting, and sliding the best shoes for a ZUMBA® class are supportive cross trainer with not much rubber at the bottom, dance sneakers or aerobic dance shoes. Ideally something without deep treads that grip the floor too much to prevent the risk of knee injuries.
Because there is a lot of side-to-side movement in a Zumba® fitness class, you should consider buying a shoe that is a "trainer" rather than "running" because cross-trainers offer lateral support. While we do not particularly endorse one brand of shoe over another and preferences are also made by an individual’s comfort level, below are some dance-fitness shoes that seem to work for this type of workout:
Nike Shox Electro
Nike Danzante Star
Nike Musique III
Ryka Intensity XT3
Ryka studio D
Bloch Dance Sneakers
Addidas Bounce
And many more!!
In addition, you also need some cushion support so you may want to also invest in some inserts for your dance shoes. Keep in mind what works for one person doesn’t necessarily work for you, you may have to trial and error before you find that perfect shoe to dance in.