Camel is designed to be small lightweight and extremely modular so that you only pay for what you use. The core of camel, camel-core.jar is small and has minimal dependencies.
On Java 6 camel-core.jar only depends on
On Java 5 camel-core.jar depends also on activation.jar and a JAXB2 implementation which typically involves jaxb-api.jar, jaxb-impl.jar and a StAX API which may be stax-api.jar and *woodstox.jar
If you wish to work with Spring, you will also need camel-spring.jar along with the spring.jar or the individual spring jars if you prefer.
For other components you may want to look at the maven reports to see the exact dependencies of individual modules.