Other cats in the cat family are usually not suitable as domestic cats. Generally, they are too big, strong, and destructive. In addition many states have strict regulations about keeping wild animals as pets. It also appears cruel to have to defang and declaw these animals to make them safe.
If you have the overwhelming urge to be around wild animals, your best bet is your local zoo. Many zoos have volunteer docent programs and you will not only be able to spend time with the various animals, but also learn a lot about them and have the opportunity to educate the public while conducting tours or participating in other public relations programs.