Um, yeah, we've found the bottom a few times.
If you've got a heavy cruising boat like we do, get a TowboatUS and/or a SeaTow membership. It will pay for itself the first time you use it -- very cheap insurance.
The various tricks for getting unstuck will depend a great deal on the type and configuration of your keel and the overall displacement of your vessel. In our case (full keel that has a gentle slop to the stern at about 27k lbs with a cruising load) by the time the boat comes to a stop -- even if we've been motoring at idle speed -- we're pretty much stuck. We've been able to kedge off a time or two, but have been forced to await a rising tide as well.
In the avoidance department, you can try to attempt all your passages through skinny water on a rising tide but that isn't always practical. Avoiding skinny water all together is also an option, but could seriously restrict where you go; there are several spots along the AICW that are good examples of this.