There are no hard and fast rules, but the rule of thumb from a purely conceptual standpoint that I like to use can briefly be summed up like this: a URI path (by definition) represents a resource and query parameters are essentially modifiers on that resource. So far that likely doesn't help... With a REST API you have the major methods of acting upon a single resource using GET, PUT, and DELETE . Therefore whether something should be represented in the path or as a parameter can be reduced to whether those methods make sense for the representation in question. Would you reasonably PUT something at that path and would it be semantically sound to do so? You could of course PUT something just about anywhere and bend the back-end to handle it, but you should be PUTing what amounts to a representation of the actual resource and not some needlessly contextualized version of it. For collections the same can be done with POST. If you wanted to add to a particular collection what would be a URL that makes sense to POST to.
This still leaves some gray areas as some paths could point to what amount to children of parent resources which is somewhat discretionary and dependent on their use. The one hard line that this draws is that any type of transitive representation should be done using a query parameter, since it would not have an underlying resource.
In response to the real world example given in the original question (Twitter's API), the parameters represent a transitive query that filters on the state of the resources (rather than a hierarchy). In that particular example it would be entirely unreasonable to add to the collection represented by those constraints, and further that query would not be able to be represented as a path that would make any sense in the terms of an object graph.
The adoption of this type of resource oriented perspective can easily map directly to the object graph of your domain model and drive the logic of your API to the point where everything works very cleanly and in a fairly self-documenting way once it snaps into clarity. The concept can also be made clearer by stepping away from systems that use traditional URL routing mapped on to a normally ill-fitting data model (i.e. an RDBMS). Apache Sling would certainly be a good place to start. The concept of object traversal dispatch in a system like Zope also provides a clearer analog.
