I wrote a Daily List for the nerd website Topless Robot that aimed to provide a comprehensive reading list for users who have never read the X-Men before. You can see the whole article here. Since you are specifically asking about storylines since 2000, that narrows it down a bit. You should definitely start with (quoted text from my article):
- New X-Men Vol. 1: "E is for Extinction" (2001)
With stories full of psychedelic pseudo-science and dialogue as elegantly complex as poetry, Grant Morrison isn't everyone's bottle of Mountain Dew: Code Red (you haven't tried Code Red? DO IT!). Love him or hate him, you have to admit that he revitalized a stale franchise when he took over in 2001. He re-opened Xavier's School to a student body, added Emma Frost (the former White Queen) to the team, and crammed enough progressive ideas into the X-Universe to fill a college lecture course. He may have not treated the characters with the respect fans feel they deserve, and I will never forgive him for his Multiple Man orgy-of-one joke, but he routed the franchise in the direction it still travels in.
- Astonishing X-Men Vol. 1: "Gifted" (2004)
Buffy the Vampire Slayer creator and geek god Joss Whedon came to comics armed with his love and admiration of classic X-Men stories. Devotees of Whedon's TV work will be pleased to know that very little was lost in translation. Whedon and the impeccable art of John Cassaday create a story that is a tonal update of the omnibus that kicked off this list. Astonishing X-Men is the X-Men done with a level of skill and attention to character not seen since the Reagan administration.
Following a massive long-term blackout of mutant births, a new mutant is born in Alaska. What follows is an action-packed game of tag between a militant group of humans who want the baby dead, the evil geneticist Mr. Sinister who wants the baby for his own nefarious purposes and the X-Men who are fighting to keep the baby safe. Filled with tense drama and stylistic ultra-violence (the black ops, claw-filled version of X-Force debuts here), it's like the '90s never stopped.
The most recent of all the big crossovers, "Second Coming" picks up right where "Messiah Complex" thematically leaves off. Much like "X-Cutioner's Song" before it, this acts as a sampler of the various characters and status quos featured in the current crop of X-Books. The crossover also features a number of shocking deaths and, that old '90s standby, variant covers. If comics are right and the '90s are in vogue, then movies should prep themselves for a whole lot more Van Damme.
Those trades act as the big mile-markers for the last decade of X-Men stories. I would also add to the list:
House of M (2005) - This is a crossover between the Avengers and the X-Men, which had enormous ramifications for the X-Universe that are still being felt, six years later.
X-Factor Vol. 1 (2006) - This relaunch of the early '90s iteration of the X-Factor title has been the most consistently excellent X-Men comic of the past 10 years. It is, however, pretty separated from the rest of the X-Universe (Multiple Man operates a detective agency with a bunch of B/C-List X-Characters) and could be read on it's own. However, picking up this and subsequent trades will help flesh out the events of "Messiah Complex."
X-Men: "Supernovas" (2006) - Acclaimed Vertigo writer Mike Carey took over adjectiveless X-Men (the one started in 1991 by Jim Lee and Chris Claremont) with #188 and, with artists Chris Bachalo and Humberto Ramos, told some very engaging and entertaining stories. His run on the book spans approximately 60 issues, this trade collecting the first five. If you are a fan of Rogue, this is a great series to start reading.
Uncanny X-Men: "Manifest Destiny (2009) - This storyarc transitions the X-Men from their Westchester headquarters to their current home, San Francisco. It also includes the milestone Uncanny X-Men #500.
Uncanny X-Force Vol. 1: "The Apocalypse Solution" (2010) - This is the first arc of the latest addition to the X-Lore. Uncanny X-Force follows Wolverine, Psylocke, Archangel, Fantomex (who you will meet if you read all of Grant Morrison's New X-Men), and Deadpool. It is thought-provoking, action-packed, and a rollercoaster ride. It is definitely worth picking up, as it is quickly become the current X-Book to beat quality-wise. It also uses brings a lot of the '90s ideas and characters back into rotation, so odds are you'll see characters you remember loving.
X-Men: Schism (2011) - This is the big event currently going on right now, and once you've read most all of the above, you can start right here. Schism is being hyped as the biggest X-Men event in a decade, and it is leading to a complete overhaul of the X-Men line (the likes of which haven't been seen since the 1991 relaunch).
The relaunch is being titled X-Men: Regenesis and Wikipedia has a very nice summary of what's to come. In all honesty, you could try skipping everything above and jumping on with Regenesis, as it's being marketed as a jumping on point.