I am a universalist in the Biblical sense of "as in Adam ALL die, even so in Christ shall ALL be made alive." (1 Corinthians 15:22) I don't see how any believing Christian can address that verse (or the entire chapter of 1 Cor. 15, actually) without being "universalist" in that way - since "all who die in Adam" means "all who ever have lived". In Mormon terms, that means I believe all who ever have lived (minus very few Sons of Perdition, who are the exception that proves the rule) will be "saved" and receive a degree of glory.
I also am universalist in that I believe exaltation is "available" for all - and I am "more universalist" than many other Mormons in that I believe we will be shocked in the end at the percentages that make up the various kingdoms. Frankly, I don't preach reincarnation, since it's not part of the Christian paradigm, but I see a "reincarnative process" in our theology that is missing completely from the rest of Christianity - that informs how we are universalist at heart.
At the very least, we teach of 5-6 distinct states of being - and one more if I am allowed to define creatively.
1) Intelligence (no idea, really, what that means);
2) pre-mortal spirit (no idea, really, what that means other than "created" by exalted parents - or what process was used in that creation);
3) Mortal human (a combination of "immortal" spirit and mortal body);
4) post-mortal spirit (a pre-mortal spirit with more memories); [*grin*]
5) post-resurrection being (which might or might not be "separated" [sorry for the pun] from);
6) post-judgment, "glorified" being (assigned to a
7) The 7th stage would be Heavenly Parent.
It is noteworthy that the first SIX stages are universal in our theology. The only one that is not universalist in every way is #7 - Heavenly Parent. It also is instructive to note that those who accuse Mormons of being arrogant exclusionists almost "universally" are less universalist than we are. That is one of the most ironic aspects of religious debate I can imagine - and it influences my frustration with conversations with others about temple ordinances. Those discussions generally are couched in terms of the exclusionary arrogance such ordinances illuminate, when, in fact, they are the practical core of our universalism.