There is a fair amount misinformation and confusion in this thread already... So, you need a good travel camera that would take decent telephoto pictures and won't burden you too much. Here are my 0.02 (and, BTW, +1 on what asp125 and Splitter said):
A lot of people suggested SLRs, which would have been a good advice a few years ago. Not today. To get a really good telephoto picture from an SLR you need a good telephoto lens. With SLRs they are universally big, heavy, and expensive. Sure, you can get one of the various plastic xx-200 or xx-300 lenses that are small and relatively light, but they all compromise the picture quality too much, especially at thetele end. And you are still carrying a big honking chunk of a camera and some non-trivial amount of glass. There is absolutely no point in buying an SLR if you don;t invest in good quality lenses, and they are expensive and big, so these days an SLR makes sense only if you are going on a photography trip. BTW, if its a once-in-a-lifetime safari, you may consider renting a good telephoto lens (like a 300/f2.8 for that trip only, those lenses cost several thousands of dollars, take half of a backpack, but shooting with them is an incredible experience). Again, if you don't know what I am talking about, maybe this is not a good solution.
Point and shoots. Great if you want to have a compact camera that would take decent photos and you don't want to be bothered with technical details. The problem is that with image quality, size, and zoom range you can have any two, but not all three. People suggested Panasonic DMC-FZ200, which is a superzoom. Good camera, but its pictures would not hold a candle to anything you can get with an SLR or a mirrorless. Its a tiny (i.e. noisy) sensor put behind a lens that is trying to do too much given the space constraints. Its good for shooting ducks at your local pond, for animals in Africa I would get something more serious that would get you a much bigger sensor and a brighter lens. If you need a good point and shoot for walking around look at the Sony RX100, which is a fantastic camera that takes pictures that are equal or better than what you can get from a cheap SLR. Why? It has a 1-inch sensor that is 4 times larger than a sensor in any other point-and-shoot. And in photography (like in other endeavours) size matters.
Now to what would be my choice for the trip- mirrorless. These are the cameras that have sensors that range from full-frame to APS to 4/3 size sensor. Someone said that a Canon G series is a mirrorless. That is incorrect, they look like a mirrorless, but the sensor inside is a point and shoot size. Good cameras, but not what you are after. By the way, Nikon 1 series is also not quite a mirrorless- the sensor size is quite a bit smaller. if you are going with 1 system, you are better off buying the Sony RX100, which is smaller, and has the same size sensor. Anyhow, in mirrorless you have a choice between micro-43 system (Panasonic, Olympus), and Sony NEX. Both are really good systems that have decent telephoto lens options. Both will be way smaller and lighter than any SLR, both will take pictures that are just as good, and probably better dollar-for-dollar. My recommendation will be the Olympus OM-D body with either a Panasonic 45-175 lens or an Olympus 75-300. With the 2x focal length multiplier of the micro-43 sensor, you get a lot of reach. And while you are at it, pick up a prime lens, either the Panasonic 20f1.7 or the 14mm (I think that's their wide-angle offer). The images you will get from thoseprime lenses will be magazine-quality and the telephoto will not be too far behind. The camera is surprisingly small, very fast, and really well-built, it's been a huge hit for Olympus and deservedly so. It has a good electronic viewfinder and tiltable screen, so you are covered for every situation. And, by the way its fully weather-sealed, which is something you will have to pay a lot more to get in an SLR. Here is the camera with a tele lens and a size comparison with one of the smallest SLRs, good luck. (Disclaimer- I shoot with a different mirrorless- a Fuji X-Pro1, but I like the prime lenses, and I like having a "rangefinder-like" shooting experience, otherwise I would have bought an OM-D as well).