Well, looks like most of the responses here cover the CR123 battery issue. I'll add my $0.02, but I'll also try to cover the other things mentioned in the OP. Oh, and this might be a lengthy post, so bear with me.
1. CR123 vs. other (for simplicity, let's say AA): For myself, I guess I picked CR123 as my flashlight standard not as much because they were superior (though in my mind they are), but rather because SureFire used them in all their lights I wanted, and I really wanted a SureFire. That said, I fully view CR123 cells as superior because: they have a longer shelf life, they give you more runtime than alkalines, they have a higher voltage which allows for more powerful lights, they're physically lighter than alkalines, they won't leak after long periods of no use (i.e., they'll never ruin the inside of a flashlight just from sitting in there too long), and they're just about as cheap as AA's if you act ahead of time and buy them online. Yes, you'll find more AA's in stores, particularly in the boonies, but personally I can only think of two acceptable reasons not to have a good number of spares on hand (by on hand, I mean maybe one set on your person, and a bunch more nearby, such as in your house, in your car, etc.): backpacking and overseas traveling, where you need to shave as much space and weight as possible. If you do a lot of these, consider AA's (though even for backpacking, the CR123's will weigh less, whether in a flashlight or as spares). Your mileage may vary, of course, so you may see other benefits to AA's, but at the end of the day, I can't personally find any truly good justification for using them over CR123's.
2. Brand: SureFire is indeed probably the best place to look for a good flashlight. I'm sure you're familiar with their reputation, so I need not say more. Inova is another good brand to look at (though in general I think the selection at SF is better). I've also heard good things about Nitecore, Fenix, Dereelight and Tiablo, though I don't have any personal experience with these. If AA's are a must for you, then from what I've seen written on these boards in reviews, I'd recommend Nitecore, then Fenix (depends on what you want from the light, though). In the end, I'd still go with SureFire.
3. Durability: I'd expect any SureFire to be top-notch here, and any Inova (minus the keychain lights) to measure up to the same level. Other than those, the best durability I've heard about was Dereelight, and I think Nitecore. Mag of course has great durability, but to get non-archaic performance out of it, the only upgrade I have any remotely first-hand experience with that I'd trust for durability is the Malkoff drop-in.
4. Water resistance: I doubt anything mentioned around here will stand particularly ahead of the pack. There are truly waterproof lights out there, but they're for diving, and I don't think we need to be that concerned about it. For everyday needs, any SureFire, Fenix, Dereelight, etc., etc., will have all the rain/puddle/dunk/splash/etc. resistance you could ever want.
5. Brightness: If you want the brightest of the brightest, then go HID; below that, incandescent, and for slightly less than scorchingly bright, go LED (incans aren't worth the lower runtime below 200 lumens to me). I imagine you'll want some sort of LED, as the 500+ lumens lights are more of a specialty-purpose thing. Most LED's these days will give you decent efficiency, and that's what's important in the end. I'll be more specific later when I outline some particular light suggestions.
6. Battery life: LED's are where it's at, and efficiency is key. Also, here's where the suggestion to use CR123's comes in again.
7. Rechargeables: Although SureFires fit just about all my other recommendation criteria, they apparently aren't great about guaranteeing a fit with rechargeables. I get the impression that their 6P/G2/C2/etc. lights tend to fit better than the newer E2L/U2/etc. models; basically, other companies will make lights guaranteed to work with rechargeables, but I wouldn't rule out the SF's altogether. I'd recommend picking your light first, and then look into rechargeable options later. If rechargeable is crucial, though, I think Dereelight has some great options for primary/rechargeable compatibility.
8. Price: You neglected to mention a price range for the light that you want. I would likely recommend very different lights if your range was either $50-$100 or $150-$200. I'm hoping you're okay with the $100-200 range, as that's where my prime recommendation will lie, but I'll try and think of something cheaper as well.
9. Emergency light: For emergency purposes, I'll likely never be more comfortable than with a SureFire (with non-clicky switch). Inovas would take a close second in my mind, followed by any of the other respected manufacturers. For emergency, a twisty switch is key, in my opinion, as well as runtime on at least one mode to be at least 4+ hours.
10. General "boonies" light: Living in the boonies myself, you'll definitely want something with some decent throw if you're going to be outside at night with a treeline more than 75 feet away. Depending on the specific environment, you may need something like a 3D mag or Dereelight DBS for the extreme throw, or you may not (in my surroundings, which are woods with various clearings, the throw of P60-compatible lamps are perfectly fine). Also, you'll want plenty of wide flood/spill outside the hotspot, in order to see things off to your side, and to navigate while pointing the light in the distance. For this, the narrow beam of, say, a Mag 3D, will be less than ideal. I'd go with something with the beam spread of a SF G2L or Inova T1. And if you can afford a Malkoff dropin, those will be even better, since they don't have a harsh line where it goes from flood to dark.
11. Mosquitos: From my own experience (and these days, this is probably about 40% of my flashlight use), mosquito hunting is most effective with an entirely diffused light; no hotspot. And the wider the diffuse beam, the better. Also, the brighter the better. My Inova T1, for example, works WAY better than my stock Mag 3D, but any light with a diffuser like the SureFire FM34 is PHENOMENAL.
12. Specific recommendations: Well, for starters, if you really need something cheap, like, sub-$50, the Inova X5 is the only thing that comes to mind. I know there are others out there, especially ones that will perform better for your needs, but no sub-$50 lights are coming to mind at the moment. You'll have to ask others if this is what you need.
If your price range is $50-$100, then I'd first recommend the SF G2L (or 6PL, 9PL or G3L for that matter). This is probably the best all-around light out there, particularly if you don't mod it in any way. It's got a nice, bright hotspot, with very wide, useable flood, and respectable runtime. Sure there are lights that do better, but not necessarily when you factor in the warranty, durability, brand reputation, reliable twisty switch, and price. Other than these lights, the Inova T1 will do fine (as well as other Inova T-series lights, I imagine), as well as Fenix lights, Nitecores (particularly the EX-10, from what I hear) and a number of others. Other CPFers might be able to give better advice here.
Hopefully you can afford the $100-$200 range, though. This is where things get interesting. The SureFire L1, for example, is a great light with two stages, great tint, good brightness, good runtime, reliable switch, etc. And with the diffuser you can buy for it, it gives you the option to have either a nice spotlight in stock form, or a perfectly diffuse light perfect for close-up use. Price: $135 (L1) + $12 (F04 diffuser) = $147.
And last but not least, THE light that you want, the light that fulfills all your requirements (save the tendency for AA thing, which hopefully you've been convinced to ignore) is the SureFire C2, hard annodized, with a Malkoff M60 drop-in and FM34 diffuser. This is the light sitting on my belt as we speak. It fills for me all the purposes you seemed to outline in your original post, and it does them better than any other light I've ever seen. The body (C2 in this case) is up to you and your tastes, of course, but I opted for the C2 because of the combat grip, which gives you a perfect grip on the light, and allows for great operation in a cigar-grip. That said, a 6P would make for a cheaper light. Anyway, the M60 drop-in is what makes this light fabulous. It's got excellent throw, the best brightness possible for a widely available LED light, and the best tint I've ever seen on any light, ever (this thing has better color rendition than either my other LED's or even my incandescents, which makes it the best outdoor light possible (at least to me). Also, since the M60 uses an optic rather than a reflector, the fade away from the hotspot to spill to dark is the smoothest you'll find out there, and effectively puts out a wider spread of light than a stock G2L or whatever will permit. And then once you add the FM34 diffuser, you have the choice to, at any time, flip between the throwy hotspot and the VERY floody diffused beam. With its brightness, diffusion, and width of beam, this light (with diffuser on) is THE best mosquito hunting light possible. Mosquitos, room-lighting, blinding your friends, you name it. It's the best. Price: $115 (C2 hard annodized) or $60 (6P) + $55 (Malkoff M60) + $35 (FM34 diffuser) = $205 or $150. And if you buy the 6P off of eBay, you could shave another $15 off of that, and bring it to $135. (...Man, this is making me want to buy another...)
So in the end, I highly recommend a SureFire 6P/C2/etc. series light, a Malkoff drop-in for it (M60 for optimal brightness, or M60L if you want the best runtime/brightness combo on the market today), and a SF FM34 beam filter. Or, if you want to skip the FM34, and can live with just flood, you could opt for a Malkoff M60F or M60LF (the beam on these is great for walks around the woods, searching for things indoors, even finding mosquitos; it is narrower than the FM34 though).
Okay, so that was WAY more than I intended to write. I really hope that at least something in it is useful, though. And that anyone who actually read it will forgive me someday...
