Extract from the Sea Kayaking Safety book:

You have heard the phrase describing being in jeopardy as being “up the creek without a paddle”.  Well, there’s at least one stage of jeopardy worse than being up a creek without a paddle, it’s being out at sea without one!

….

There is heated debate in the paddling community about whether paddle leashes are a help or an added safety risk. Not everyone likes using them, as they can get in the way and have the potential to entangle the paddler, especially in active waters. These paddlers prefer having a backup paddle on hand instead. Others feel strongly that leashes are important, however they also recommend having a knife along to cut themselves free if necessary.

A good compromise is a short paddle leash that connects from your wrist to the paddle shaft with a quick release mechanism in it.  This has minimum entanglement risk, is unobtrusive, can be attached if things are starting to look dicey and can be quickly detached if needs be.