For some idea of this spectrum, I'll list examples of birds which match the categories listed above: ostrich, chicken, pigeon, cuckoo, (no example given), woodpecker. Claw morphologies across modern groups seems to be indicative of degree of arboreal foraging--the more curved the claw, the more arboreal the bird.
Glen & Bennett measured the claws of several Mesozoic taxa, incuding Archaeopteryx, Microraptor, and Confuciusornis. Of all the Mesozoic birds sampled, only Sapeornis fell within the "predominant arboreal forager" category. All of the other ancient avians fell below that grouping, and were generally found to be either "dedicated ground foragers" or "predominant ground foragers." Not surprisingly, Caudipteryx fell within the "ground-based bird" category, while Pedopenna, Microraptor, Archaeopteryx, and Jeholornis were strong terrestrial in their habits.
The paper raises a number of questions. First, the very idea that birds "escaped" to the trees must be abandoned, if they did most of their business on the ground. One might be tempted to believe that, in China anyway, large predators did not exist to yet to threaten these largely terrestrial birds, but the recent discovery of dromaeosaur tracks in China indicates that a Deinonychus-sized predator existed alongside those smaller avian critters. Also, the motivation for the evolution of the reversed hallux must be questioned. While generally thought of as a means to perch, I think the idea that Archaeopteryx and its kin were spending a lot of time soilside downplays the importance of the hallux. Why did the reversed hallux evolve if trees were not the enormous draw we once thought they were?
These are important questions, and I'm happy to see that Glen & Bennett have brought them up. The trip from the ground to the trees may have been a lot more complicated than we awknowledge, but that's fine by me. It just means there's so much more to discover!
Hat-tips to Will and Brian, of course, for letting me know this story existed.
Glen, C. L. & Bennett, M. B. (2007). Foraging modes of Mesozoic birds and non-avian theropods. Current Biology 17(21): published online.
Li, R., Lockley, M. G., Makovicky, P. J., Matsukawa, M., Norell, M. A., Harris, J. D. & Liu, M. (2007). Behavioral and faunal implications of Early Cretaceous deinonychosaur trackways from China. Naturwissenschaften: published online.