Legendary birds: Multiple, both genders
Mew: Only one, female
Mewtwo: Only one, male
Legendary Beasts, Ho-oh, Lugia, and Celebi: Multiple, although only one immortal original, both genders
Regi Trio: Multiple, genderless.
Groudon: Only one, male
Kyogre: Only one, female
Rayquaza: Only one, female
Deoxys and Jirachi: Multiple, both genders
Latios and Latias:Multiple, both genders (Male is Latios, female is Latias, obviously)
Lake Trio: Only one of each, all female
Dialga and Palkia: Only one of each, Dialga=Male, Palkia=Female
Heatran: Multiple, both genders
Cresselia:Multiple, female only
Darkrai: Multiple, both genders
Manaphy: Multiple (just very, very rare), all female
Phione: Multiple, all male
Shaymin: Multiple, both genders
Arceus: Only one, female
Manaphy: maybe a few, not too many, like maybe two or three for a major ocean like the Pacific. Different genders.
Phione: More of them than Manaphy, also more commonly sighted. Different genders.
Legendary Trios: A few of each, either gender. Only one immortal original.
Darkrai: One, maybe two, male.
Cresselia: Same as my opinion on Darkrai, except female.
Heatran: One or two for each major volcano, like Pompeii or Mt. Saint Helens. Different genders.
Shaymin: maybe a few, not too many, like maybe two or three per continent or something. Either gender.
Latios/Latias: Maybe a pair per region. Genders obvious.
Arceus: One, genderless.
Mew: Multiple, all less powerful than original, mostly female.
Mewtwo: One, Male-ish, but genderless.
Deoxys: Many, genderless.
Jirachi: One or two, can be either gender.
Celibi: Infinite number, each from different teeny fractions of time. Either gender, although don't breed.
Trio leaders: Multiple, although only one immortal original, both genders.