Botanically speaking, the two most common jasmine species used in perfumery are Jasmin Grandiflorum and Jasmin Sambac. There is also Jasmine Auriculatum, which is less commonly used in perfumery, but is unique and quite different from the other two types. Than there is also star jasmine, which isn't technically a jasmine, thought he flowers look and smell very much like one. The latin name is Trachelospermum jasminoides (it's from the genus Trachelospermum, not Jasminum). I don't believe there is an essential oil of that, but it recently became quite a popular note in some commercial perfumes (i.e.: Opium Fleur de Shanghai). It can be tinctured or macerated or infused by hand though (which some artisan perfumers who are very skilled and crafty actually do themselves).
Jasmine Grandiflorum is the richest and deepest of all jasmines. It's very rich with indoles, and has a deep, penetrating aroma.
Jasmine Sambac is lighter and fruitier, and is reminiscent of gardenia in it's sheer heady tropical fragrance.
Jasmine Auriculatum is intesnely green, and only slightly floral. In fact, it has an almost grassy smell. It's very tenacious.
Star Jasmine (which as I mentioned earlier is not really jasmine at all) has a light, airy, white floral aroma, lighter even than the sambac. It is not surprising that it's only gaining interest from perfumers recently - because of the increasing demand for the "light" floral scents.
Now, I know I haven't truly answered your question, and didn't even give examples of perfumes - but to me, many of the perfumes that claim to be using jasmine smell too artificial. It's hard to find a good jasmine note in my opinion - unless it is highly natural, and this seems to become more and more rare. i am going to think up some examples and post more later...