Mypoppy31 - Nowadays most mid to higher end P&S cameras have AEB. How good that is, can vary - but two of the higher end Canons, the S95, for a Semi-Compact camera, and the SX30, for a bulkier Bridge Zoom, have AEB at 3 shots across +/- 2EV at 1/3EV adjustment increments.
The 35x zoom SX30 has a viewfinder, so can be hand-holdable for AEB, but the LCD only 3.8x zoom S95 has no viewfinder, so probably needs a firm rest or tripod for AEB.
The SX30 has a 1/2/3" sensor and doesn't do RAW (without CHDK) - while the S95 has a 1/1.7" sensor and does have RAW as standard.
Of course, many other Brands of cameras also have AEB in various sized and equipped models.
Check that for AEB cameras do at least +/- 2EV, and are incrementally adjustable at 1/3 or 1/2 EV settings.
Fuji's current cameras only do +/- 1EV on AEB, so aren't a great lot of use for AEB-style HDR. With my HS10, I can, with tripod, use the onscreen exposure bar, for sequential +/- 2EV by 1/3s sets of 3 or 5, etc, images. But some would find that most inconvenient.
Dave.