Each and every technology presented here has its drawbacks. You should carefully consider you needs, the services your exposing and the objects you'll be sending over the wire when choosing a technology.
When using RMI, it's not possible to access the objects through the HTTP protocol, unless you're tunneling the RMI traffic. RMI is a fairly heavy-weight protocol in that it support full-object serialization which is important when using a complex data model that needs serialization over the wire. However, RMI-JRMP is tied to Java clients: It is a Java-to-Java remoting solution.
Spring's HTTP invoker is a good choice if you need HTTP-based remoting but also rely on Java serialization. It shares the basic infrastructure with RMI invokers, just using HTTP as transport. Note that HTTP invokers are not only limited to Java-to-Java remoting but also to Spring on both the client and server side. (The latter also applies to Spring's RMI invoker for non-RMI interfaces.)
Hessian and/or Burlap might provide significant value when operating in a heterogeneous environment, because they explicitly allow for non-Java clients. However, non-Java support is still limited. Known issues include the serialization of Hibernate objects in combination with lazily-initialized collections. If you have such a data model, consider using RMI or HTTP invokers instead of Hessian.
JMS can be useful for providing clusters of services and allowing the JMS broker to take care of load balancing, discovery and auto-failover. By default: Java serialization is used when using JMS remoting but the JMS provider could use a different mechanism for the wire formatting, such as XStream to allow servers to be implemented in other technologies.
Last but not least, EJB has an advantage over RMI in that it supports standard role-based authentication and authorization and remote transaction propagation. It is possible to get RMI invokers or HTTP invokers to support security context propagation as well, although this is not provided by core Spring: There are just appropriate hooks for plugging in third-party or custom solutions here.