Which liturgical rites (forms of Mass) are presently used in the Roman Catholic Church? A liturgical rite is a way to celebrate the Mass. At least for the purpose of this question I will assume this meaning of the term.

The standard way Mass is celebrated by Roman Catholics is in the Roman Rite. This normally refers to celebration of the Mass originally based on the Missale Romanum from 1970 as commissioned by Pope Paul VI (there have been recent modifications); this happens (always?) in the local language. The so-called extraordinary form of the Roman Rite is the Tridentine Mass, celebrated in Latin, nowadays according to the Missale Romanum of 1962.

Aside from these two liturgical rites (which some will say are technically just two forms of a single rite), I have seen mention of others, such as the Ambrosian Rite, Anglican Use, and Zaire Use. Which forms of Mass (rites) are presently used within the Roman Catholic Church? How can one characterize them, and where are they used?
How can one characterize (a rite)?

A rite represents tradition about how sacraments (not just Mass) are celebrated. As the early Church grew and spread, it celebrated the sacraments as would be best understood and received in the context of individual cultures, without ever changing their essential form and matter. 

Which forms of Mass (rites) are presently used within the Roman Catholic Church? and where are they used?

Counting novus ordo and tridentine as a single rite, there are totally 5 western rites and 22 eastern rites (with five eastern liturgical tradition). The complete list of functional rites and their jurisdiction can be found at gcatholic.org.

Please see Wikipedia article titled List of Catholic rites and churches for the list of defunct rites, But I really doubt that this is an exhaustive list of defunct rites.