Well, in my humble opinion, the whole thing about having legendaries one-off and genderless in the games is probably to prevent people from breeding armies of legendaries and thus breaking the game. ^_^;
Biologically, it is ridiculous to think that these things don't have genders and generations. Even the games prove that legendaries do exist as more than one creature, as some of the frontier brains obtain legendary PokeMon. (And yet, you aren't allowed to use any in the frontier. X_x They're cheating against their own rules!)
Deoxys and Jirachi are alien organisms - Deoxys is an anthropomorphized, sentient creature which may has apparantly evolved from a Virus. Both of them have 'hibernating' forms - Deoxys can (when travelling through space, for instance) let go of the organic matter it generated and transform into its purest core form - as long as that core is left intact, Deoxys may easily regenerate (like a Starfish, for instance.) Jirachi seems to encase itself in a layer of meteorite-like rock as it hibernates.
The Weather Trio (as I personally call the three 'super-ancient' PokeMon) also have hibernating forms. Like the legendary birds they seem to have an effect on the climate - the climate influence in the birds' case is only relevant apparantly to a specific Articuno/Zapdos/Moltres trio which have, apparantly, more elemental power than the rest of their kind, and due to the particular location of the Shamouti island region - the ocean currents are affected if their equilibrium is ever disturbed. (shrugs)
The legendary beasts... I'm not certain about those. I haven't seen the particular episode which is the Anime's excuse for their origin, but fact is that they are quite ancient. Three of them were revived by Ho-Oh, but does that mean that's ALL three that ever have been? Maybe they're just so rare, that the three revived ones are the ones that gave the species its legendary status?
Mewtwo's a definite one-of-a-kind, being manmade. Unless if it splits like Neifirst in Phantasy Star 2 and lets his better half out in a body of its own. xD
I dunno. I think the almighty turkey that is Ho-oh is way overrated, but the anime DOES treat it as a god - making it an exceptionally rare sight. However, Ho-Oh is a Phoenix. Meaning, it dies, but is reborn from its ashes time and time again, so I doubt that it has the actual need to procreate. However, I'm still wondering if Ash was delirious when he saw that shining Ho-Oh in the first episode, or if Ho-Oh simply dived into a bucket of gold paint before taking that flight. ^^;
The Latis... There's a whole damn lot of them. And I do mean a whole damn lot. Movie 5's introduction reveals that the two guardian Latis that remained were simply the only two that stayed of a whole flock, out of care for the old couple that considered them their children when they were found, hidden in human form, on a beach (The dubbed version of course cut the sequence and utterly butchered the back story, but one of the nice things about anime is that you can ignore the atrocities of the dub and consider the original. xD)
As for the Regis, I've put together a theory regarding them and the possibility that more than one exist - one that you can find
here.
