With that you dismiss the vast range of point-and-shoot cameras, film-based or digital. A typical point-and-shoot camera like Canon's PowerShot SD450 ($450; www.canon.com) has a three-power zoom, with the maximum pull roughly equivalent to a 100mm lens on a 35mm film camera. Fine for portraits, but not by any means a powerful lens. Even Canon's top-of-the-line PowerShot Pro1 ($800) has a lens that maxes out at about 200mm equivalent, which does get close to being a "real" telephoto but still isn't that powerful. You need at a minimum a lens that's equal to 400mm equivalency in a film camera. And that means you have entered the world of single-lens reflex (SLR) cameras, and interchangeable lenses.
So you have two routes. One is to rummage around eBay and get yourself a 35mm film-based SLR, such as a Nikon F100 (expect to pay $400 to $500 for one in very good condition; www.nikon.com), and some lenses. I suggest a basic lens setup that starts with a f/2.8 24mm lens for wide-angle work. Ideally, you then add a decent fast zoom in the middle focal lengthsTokina's 80-200mm f/2.8 is great and not too outrageous at around $600, street price (www.thkphoto.com). Finally, get a BIG telephoto; Nikon's 500mm f/8 mirror lens is not bad, for around $700.
Yes, I know we are talking big bucks here. But if you don't spend them, wild animals will look like little bugs in your pictures.
You can go the digital SLR route, too. Canon's EOS 10D has 6.3 megapixels of resolution and sells for a not too outrageous $750. All the lenses mentioned above, in Canon mount, will work. And because of the physics of capturing a digital image with this camera, you get a bit of a bonus in lenses. The Canon EF 55-200mm f/4.5-5.6 II USM ($225), for instance, covers a 35mm equivalent zoom range of approximately 90-320mm. And 320mm is a fairly potent lens.
Read "Cameras Explained" for the nuts and bolts of all-things photographic.