Roger, I can't speak for everybody else who's replying (and thank you, Chris and Gail and Susan and Lance), but I'm reserving the term "dramatic monologue" for a pretty specific situation. A dramatic monologue is a persona poem--a character who's not the poet is being created or borrowed--and in general it's also that character's half of a two-person exchange.
In some cases the speaker is speaking to himself (and us) only, and those are soliloquies, strictly speaking, rather than monologues. But maybe that's a needlessly picky distinction.
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