My colleague covers the major points above, but here are a few other bits of info:
In addition to the live-action specials, there's also a 7-part animated serial called Dreamland being shown in the UK as well, with David Tennant and Chancellor Gorkon from Star Trek VI doing voices. The running time is about an hour total and it's assumed it'll be released to DVD eventually. This starts tomorrow (Nov. 21). Although technically only viewable in the UK, I would assume someone will be naughty and post it elsewhere.
The Waters of Mars is scheduled to air in the US on BBC America on Dec. 19, followed soon after (around Christmas) by the final two specials featuring David Tennant). We won't know the exact dates until closer to broadcast, based on when the BBC decides to air them (presumably Christmas Day for the first, and then either Boxing Day (Dec. 26) or around New Years for the second). The Waters of Mars aired in the UK last weekend so there's about a month's lag, but the last two specials appear set to air around the same time in both the UK and US. The last two David Tennant specials are called The End of Time Part One and The End of Time Part Two; the former is technically considered the Christmas special but it's doubtful that it'll have the same festive atmosphere of the first three.
(And one thing to note - the show has moved to BBC America and won't be on Syfy anymore. If this is a problem, all the specials will be released on DVD and Blu-Ray in February. The Next Doctor is already available on standard DVD (including an hour-long music concert extra that includes a never-broadcast-in-America mini-episode called Music of the Spheres), while Planet of the Dead, the first DW to be shot in HD, is available on both DVD and Blu-Ray. There are mixed reports as to whether Next Doctor will be included on Blu-Ray in February or remain standard DVD.)
As for the next full season, which introduces Matt Smith as the new Doctor, we won't know for certain until the spring when it will air (again on BBC America), and there's talk they might split the season into two halves due to some major sporting events the BBC is covering in 2010.
The new season is seeing regime change, with Stephen Moffat (who has won 3 Hugo Awards for the show) taking over from Russell T. Davies. RTD has stated that he will continue with Torchwood, however. As noted, though, there's been no timeframe given for a 4th season, and odds are it won't be for awhile as the BBC will probably want to focus on launching Matt Smith as the Doctor. In the UK it's not uncommon for gaps of several years to occur between seasons, so there's no pressure to get the show on by such-and-such a time. The fact there is no filming for Torchwood going on at the moment would suggest we won't see anything until at least the fall of 2010. John Barrowman is shopping around for US TV roles -- apparently he's joining Desperate Housewives for a bit -- so that tells me they won't be rolling on Torchwood S4 in the immediate future.
Alex