Floating in the Dead Sea is a highlight of any visit to the Jordan. At over 30 percent saline, the water can sustain very little marine life but it's incredibly buoyant and makes for the ultimate floating experience, even if it feels rather like taking a bath in salad dressing. Avoid getting the water in your eyes, don't stay in for more than 15 minutes, and make sure to rinse off when you get out. Be prepared for major stinging sensations if you have a cut or skin rash.
The Jordan side of the Dead Sea is not as built up as the Israeli side of the water but there are several vast luxury resorts, including a Kempinski and a Movenpick, that have private access to the water and classy spas that make use of the local mud and minerals.