If you want RTA is offering now a Round trip on the see with the Water Taxi. Starting at the Jumeirah Public Beach it goes passing the World Islands and Burj Al Arab up to the Palm Jumeirah and the Atlantis Hotel. The price is on 150AED per person and it operates with 4 passengers minimum only.
In the end this is not really cheap and if you take the tour of the Dubai Ferry Boat from Dubai Marina to Ag Ghuhaiba station at the Dubai Creek you have for 50AED per person the probably better choice even if less exclusive.
If you want to try out the Water Taxi Round trip call RTA on 800 9090 to book it.