Ed, I talk a lot about finite verbs in DOING GRAMMAR. Essentially, I use the idea of finiteness to differentiate verb phrases that can be predicates from other types of verb phrases. A clause has to have a noun phrase that functions as a subject and a FINITE verb phrase, that is, a verb phrase in which the first word in the main verb constituent shows either past or present tense form (and agreement). I find finiteness a useful concept. Not only does it allow you to define clauses, it also allows you to explain participial phrases, infinitive phrases, and gerund phrases as nonfinite verb phrases.