People will have to forgive the lack of exact quotations; I've had some computer problems, and the machine I'm on now isn't particularly high-performance and the multi-quote feature seems to bugger things up more than anything else.
So. I did not know that the U.S. Coast Guard was part of the armed forces. I always figured them to be a maritime version of the FBI or something along those lines, and I see on their website that their duties do include law-enforcement (in my defence, the Canadian version of the Coast Guard, which is the one I'm most familiar with, is entirely a civilian affair, answering to the rather non-threatening Department of Fisheries). So the Coast Guard's patrol, anti-piracy/smuggling and search and rescue duties are rather similar to the functions we've seen Starfleet vessels carry out. Their website also states they don't engage in combat operations unless the country is on domestic war-footing (in which case in answers to the Navy), which is also like Starfleet in that the organization only takes on a purseful combat footing when at a time of war (and the entire fleet only mobilizes for a major conflict, since much of Starfleet was going about their usual business during the conflicts with the Cardassians and the Tzenkathi). So, if the Coast Guard could be a military organization almost since its inception, yet retain a distinctly less martial mindset owing, no doubt, to it's chartered mission which emphacizes things like search and rescue and coastal protection against smugglers and such, then Mack's idea of a demilitarized military, as bizarre and on the surface self-contradictory though it may seem, actually has some merit to it. And if such an entity exists contemporarily, then I must admit it becomes a lot easier to see Starfleet as a kind of more evolved, benevolent military organization.
That being said (you knew that was coming, didn't you?), I still don't think it's accurate to define (though not describe) Stafleet as a military conventionally speaking, or at least as not just a military. Starfleet's stated purposes are just too different, even from an organization like the Coast Guard, and its acutal military functions too relagated to the background. Even 'military plus' seems to give the wrong emphasis on the organization's priorities. They're less military than an army, but more than, say, a citizen levy. I would suggest looking at Starfleet as a hybrid, part military, part civilian--not in terms of personel, who are all uniformed, but in terms of pursuits (and to those who said exploration was part of the mandate of past militaries... they didn't explore, they conquered; they didn't wander the oceans for the love of discovery, but for economic and martial gain in conquering new lands and subjugating the people they found. Not quite Starfleet). In particular, I think this discussion has revealed an over-emphasis on form over function. Starfleet has the form, but its military function is just one of many elements of what it does. On the flipside, one could point out a number of comteporary 'organizations' that lack uniforms, strick ranks, legitimate state backing, the ability to hold court-martials, etc... and yet are still, for all intents and purposes, military organizations (Hezbollah, etc.). What someone does is more important, I feel, than how they advertise themselves. So it's not wrong for Picard to say that Starfleet isn't (just, or primarily) a military organization (particularly when tasked with exploration), because clearly he feels that its purposes are not militaristic and has conducted himself appropriately... just as it's legitimate for Sisko to say that he's a soldier, because that's clearly the role he sees himself in this large, multi-purpose hybrid organization, and indeed he spent a lot more time in combat.
Onto some other points... some posters have expressed amazement at the idea that the Federation would defend itself with Stafleet, which is comprised, as we know, of all kinds of specialists, including scientists, engineers, medical professionals, security guards, etc. But the onscreen evidence shows that this is exactly the case. In all combat situtions, particularly the Dominion War, who has been doing the fighting? Sisko and Worf, certainly... but also Dax (both of them), Bashir, O'Brien, Nog... and they've managed to hold their own against so-called 'specialized' combatants like the Klingons and the Jem'Hadar. Clearly, all Stafleet officers are expected to meet some basic standard of combat readiness, just as I imagine they should all be familiar with basic ship's functions and science even if outside their area of specialization. Presumably that's part of the function of the Academy, to give cadets a solid grounding in all fields as they look to specialize. This basic training, then, seems quite sufficient for the purposes of their secondary role as soldiers when conflict situations arise. Let's not overemphacize the importance of training, either. Over the last few years, we've seen groups whose training regimens usually involve a few months in camps out in the desert or mountains fight better trained, better equipped, and better supported forces to an effective stalemate, on account of more flexible tactics, better motivation, and, unfortunately, a total disregard for any kind of rules of engagement or ethics generally. Starfleet is well equipped, well supported, apparently not too shabbily trained as I said above, and also has the flexibility and motivation factors working in their favour. The whole thing about creating a brotherhood, the need to trust that the guy (or gal) next to you won't break and run, isn't really applicable. For starters, the cynic in me recognizes that the whole 'brotherhood' spiel is really a way of trying to motivate soldiers who frequently don't want to be in combat situations--either because, historically, they've been conscripted into a fighting force, or because they're essentially paid mercenaries fighting for causes that seem abstract or otherwise not worth the sacrifice of their lives. The reasoning is that while you might not care about defeating commies in some distant country, or whatever the cause du jour for Iraq is, but you do care about the people firing on your buddies. Starfleet, in contrast, is not only an all-volunteer force (who aren't in it for the money), but they're also idealists; when they fight, it's because they strongly believe in what they're doing. In the Dominion War, they fought to defend their homes and way of life, which is plenty motivation. Most of the time, they also know that combat was the absolutely last recourse of their superiors, so they're fighting not because some politician got impatient, but because there was truly no other choice. Also, a soldier on a modern-day battlefield might have the option of dropping his rifle and running in the opposite direction, but there's really nowhere to run when your ship or space station is being invaded... or when facing an opponent of the size of the Dominion.
Ground forces. Some posters (and I again apologize for the lack of quotations here) said ground forces were necessary, suggesting that's what we finally saw in AR-Something. Apart from there being no evidence that these weren't just regular officers who'd pickled on the frontlines, and that we'd never seen anything like a regular soldiery/infantry before or after, ground forces just don't make much sense in the setting. When you have starships that can devastate a planet from orbit, being a ground trooper is somewhat like bringing a spork to a tank fight. Recall how many caveats were in effect to permit AR-Whatever to take place; recall, also, that other instances of ground combat all took place under special circumstances ("Rocks and Shoals", both starships had crashed without support; "Starship Down", the presence of the Founder precluded the Dominion from just blasting their crashed vessel from orbit). Most of the face-to-face combat that I would envison takes place in this setting would be ship-to-ship (or ship-to-station) boarding actions.
Finally, the whole 'surrounded by enemies' thing, as supposedly requiring a standing specialized soldiery. I don't agree at all. First of all, there's Starfleet, which, as had already been said, has been shown more than capable of holding its own against the professional soldiery of its foes. Secondly, let's keep in mind the sheer size of the Federation. The Romulan army is made up only of Romulans, supplemented by Remans and maybe some other subject species. Klingons, same thing: mostly Klingons. Cardassia, Tzenkath, the Tholians... they're all empires based around a single species, and even if that particular species is very populous (as the Klingons must be, to be killing themselves off so often and still remain so potent), they still have a numerical upper limit. Who defends the Federation? Humans, Vulcans, Andorians, Tellarites, Trill, Betazoids, Rigellians, Capellans... it's a state with hundreds of species, thousands of worlds. The Federation can easily get away with having a much smaller proportion of citizens capable of engaging in combat because their overall population is absolutely massive. Think of the United States in WWII. It was a terrible mistake to attack the Americans not because of the military they had at the time, but because they could mobilize massive population and production infrastructure into expanding and supporting that military. We didn't win World World II because the Germans were cruddy soldiers--they weren't--we won because we had so many more countries, with populations the size of the United States of Russia, that the German lines were choked with bodies and still we kept on coming (moreso on the eastern front, admitedly). Similarly, the Federation at war is capable of mobilizing enormous resources, which is why it was able to fight--at the very least--Cold Wars eventually flaring hot against the Cardassians and the Tzenkathi and still be able to conduct normal operations most elsewhere, or why it was able to take massive losses at Wolf 359 without apparently a concomitant weakening of its interstellar position. Consider who has really threatened the Federation: the Dominion, which was as large (if not bigger) as the Federation, and the Borg, whose superior technology was such that numbers became meaningless. It's an elephant, and you only attack if you've got a number of lions on your side to make up for its size.
Fictitiously yours, Trent Roman
lol. So perhaps it isn`t a)paramilitary or b)military. 
