It was the great 16th-century mystic of Safed, Rabbi Isaac Luria (Ha-Ari or The Lion), who instructed that on each of the seven nights of Sukkot one of the great Biblical leaders be invited into the sukkah. Accordingly to kabbalistic thought, each of these seven men evoked or represented one of the sefirot, the mystical aspects and emanations of God. Of the ten sefirot, these seven are in contact with the created world — hesed (loving kindness, gevurah (power), tiferet (beauty), nezah (endurance), hod (glory), yesod (foundation), malchut (majesty). Rabbi Luriah taught that through these seven physical emanations, personified in the seven great guests, one can reach up to the unfolding aspects of God's presence in the world.

There are many colorful posters one can buy, like the one below, which illustrate the characters and kabbalistic traits of all the guests.

New-age Renewalists have picked it up because it's mystical and colorful and lends itself to feminist reinterpretation. Versions of the Ushpizin invocations have proliferated which place Jewish female icons alongside the traditional male ones. This parallels the inclusion of the Imahot (the Foremothers Sarah, Rachel, Rebeccah, and Leah) alongside the traditional Avot (the Forefathers Abraham, Isaac, and Jacob) in the Amidah.

I have never been a guest in any sukkah where the hosts performed the ushpizin ritual. I've led it myself a few times, but I have never had my own sukkah so I haven't been able to do so consistently. I really love the whimsey and imagination of this ritual, and the reiteration of the symbolic attributes which connect us to our ancestors, and I hope one day I can invite both sublime and ordinary guests into my own sukkah (just as I hope one day to host my own Passover seder and do it the way I want to).

The Hebrew Language Detective blog traces the word "Ushpizin" to an Indo-European root.

. . . . Also interesting, is the number of seeming opposites that derive from this root. For example, both the English "host" and "guest" have their origins here. Even more striking, there are words with a positive connotation - hospitable, hospice and hotel, but also negative ones - hostile, hostage and host (as in an army). This was due to a tension in relation to guests: on the one hand they were to be treated kindly, but on the other hand they were strangers and to be viewed with suspicion.

UPDATE: Breslovers like to spend Rosh Hashanah in a Ukrainian town where Reb Nachman is buried. Here is a blogger's account of his trip, in chronological order:
On to Uman
Visiting the Holy Baal Shem
From Mehzbehz to Uman
Uman Uman Rosh Hashanah