The writeup above is an accurate picture of the truth in the White Wolf world as it is now. But, at one time, this was not the truth. This shows the unfortune tendency of early White Wolf products to contradict each other. That was fine for "rumors and player information" but was completely unacceptable in gamemaster information. (They "borrowed" a well known Ars Magica character named "Grimgroth" for their Tremre clan book, but got every single detail about him wrong.) I've heard that now they're much better, and from what I've seen they are, but this is why I stopped buying their products many years ago. (Pardon me for wasting a paragraph to flame. They occasionally touch on an old pet peeve of mine.)
In the Ars Magica universe the founder of House Tremere died in 861. He was the youngest of the founders of the Order of Hermes, and the least powerful. He was, however, very crafty. He devised a dueling method (certamen) to be used to settle conflict in a non-lethal manner. And of course, he was a master. In the interests of forming an organization of mages who would inevitably squabble, it was accepted. He formed a group of individuals with a tight hierarchy, and created a political machine. He was the last living founder of the Order and by 848 he had nearly taken control of the entire Order.
Then came "The Sundering" which struck Tremere and his underlings with an inexplicable malady which rendered them either mad or stricken with violent urges. This caused Tremere's politcal machine to come to an end. Eventually, the curse was lifted but Tremere had to agree to not bring retribution (and the knowledge of who did it has been erased from both records and the memories of those involved). Tremere died not long after (in the scale of a magus' life) in 861.
House Tremere was at the forefront of "The Schism" war which brought about the downfall of "House Diedne" and their expulsion and the pogrom that followed. During this war, Tremere lost nearly half of its membership.
The vampirism episode that is mentioned in the previous writeup does appear in the universe of Ars Magica, but its mention in the official books is very brief. Basically the official story is that some members of House Tremere were found to have been experimenting with becoming vampires in order to gain immortality, but their plot was discovered and they were entirely wiped out. While that is probably not the entire truth, the White Wolf books make it sound as if the entirety of the House Tremere were later turned into vampires.
Part of the reason for the short treatment of the vampiric Tremere in the new official works of Ars Magica is that they don't want to use any White Wolf material than they must. The two systems could have merged well, the original Vampire: the Masquerade books mentioned that human mages carry a grudge against the Tremere vampires. The Sabbat book makes mention of a group House Tytalus (an Order of Hermes house formerly closely related to House Tremere) mages seeking revenge on the House Tremere. Many signs pointed to the two systems eventually merging. I was mildly disappointed that they never delivered on this promise, but I'm quite irritated when they use information from Ars Magica without regard to the world which they've built there. When you write a fact down in a fictional world even the simplest mistake shakes your belief in the system. For those veterans of both systems, it's difficult to separate "Story according to Vampire" from "Story according to Ars Magica." A terrible shame.