Optical vs. Digital
Optical zoom lenses are the best, because they are using the lens optics to magnify the image. A digital zoom simply crops the image so it looks bigger, and you subsequently loose resolution. Most compact point-and-shoot digital cameras have a lens with a 3x or 4x optical zoom; some small ones can have up to a 7x optical zoom, though the optics aren't as good. If you don't mind a slightly bulkier camera, an ultra zoom with a zoom lens between 12x and 20x, is a good choice.
Wide Angle vs. Telephoto
Wide angle lenses are key for panoramic shots or for group shots in tight confines. Telephoto lenses are great for wildlife shots, such as a humpback whale off the coast of Alaska or an elk in Rocky Mountain National Park. Cameras with a 3x optical zoom usually have a focal length of 37 mm to 105 mm; 35 mm is OK, but not great, for wide angle. Ask the salesperson if there are any 4x or 5x optical zoom cameras that have a wide angle lens of 24 mm or 28 mm, such as the Panasonic TZ5 and Canon G10.
If you are looking at increasing your zoom, some cameras can take a teleconverter lens that will increase the optical zoom; these teleconverters typically run around $150 and are specific to camera models.
SLRs
A single lens reflex (SLR) camera will offer the best photo quality, as well as the ability to change lenses depending on your shooting needs. In this case, you can get a wide angle lens, like a 24-70 or 17-55, and a telephoto lens, like a 55-200 or 70-300. Another option is to get an all-in-one type lens. While these lenses aren't good for low-light photography and typically have variable apertures, they are relatively compact and good for most general photography. Examples include the Nikon and Canon 18-200 lenses, the Olympus 18-180 and the Sony 18-250.
