The overall trend of Marvel for the previous decade has been to break up their storytelling into 4-6 issue chunks of story arcs. So that sorta means that every 4-6 months of a title, you'll get a relatively decent jumping on point. Some titles, like Uncanny X-Force, build from storyline to storyline, forming a massive narrative. Others, like the recent Daredevil series, are comprised of 1-2 issue arcs with very little overarching plot. That being said, looking at the comics coming out in February 2012, I'd say that the following are fairly self-contained and accessible to new readers. Also note, every Marvel Comic has a recap page that gives the ground work of what's gone before as well as headshots of every character, making them identifiable.
Secret Avengers #22 - This issue is the beginning of a new storyarc with new writer Rick Remender. This is the black ops Avengers team and, because of that, rarely interacts with the wider Marvel Universe. It does star some of the more oddball heroes of the Marvel Universe.
Ultimate Comics Spider-Man #7 - This is set in the Ultimate Universe and stars Miles Morales, who became Spider-Man after the death of Peter Parker (in the Ultimate Universe). So far the series has been fairly self-contained; Miles Morales is new to being a hero so the series treats this established universe with fresh eyes.
Scarlet Spider #2 - I'm going out on a limb here, but I think you can get this knowing the basic premise: Peter Parker has a clone that was raised in a lab and has an understandably less moral outlook on life. He now lives in Houston. The mantle of Scarlet Spider is kind of a continuity nightmare, but this is the second issue of a new iteration of it...so I think it's readable.
Amazing Spider-Man #679.1 - This comic has been fairly accessible for the length of Dan Slott's 2 years on the book. He does stand alone stories and smaller two-part arcs in between larger stories, so there are more jumping on points than other Marvel Comics. It's one of the more "classic" feeling Marvel Comics out there.
Daredevil #9 - Light-hearted, well written, street-level, swashbuckling action with the strongest art in comics. There are some long running plots, but the writer does a great job of catching readers up and making sure that the long running plots run underneath accessible, shorter main stories.
Some of the Marvel Comics out right now are in an awkward stage: they're relatively new but have already built up enough continuity to be confusing, and the trade paperback collections of their first few issues won't be out for a few months. Back issues can be bought on Amazon, or digitally at ComiXology if you have a tablet or smartphone.
Wolverine & The X-Men - A fantastic series that is rooted in the past 7 years of X-Men continuity, but it's the perfect mix of a fresh take and a familiar setting. It's the best jumping-on point the X-Men have had in a long time, and the recap page should provide enough background.
Uncanny X-Men - Similar to Wolverine & The X-Men.
There are also a number of collected editions that can be read that provide nice entry points into the current Marvel Universe.
Thunderbolts: Cage - This collects the start of the current run of Thunderbolts by writer Jeff Parker. This series follows a group of super villains as they attempt to rehabilitate as a super hero team in order to gain freedom.
Uncanny X-Force: The Apocalypse Solution - This is the black ops X-Men team. It provides a crash course in X-Men history through a new set-up, roster and mission. Uncanny X-Force has been one of the best Marvel Comics of the past decade, and it's initial 18-issue mega story is self-contained and epic.
Fantastic Four by Jonathan Hickman - Jonathan Hickman has been weaving an incredibly dense and rewarding sci-fi epic with the Fantastic Four for a few years now, and his run starts here.
Avengers Academy: Permanent Record - This is the first collection of Avengers Academy, which is almost exactly what the title suggests. Kids learning how to be Avengers. The students are all new characters.
Reaching back a few years, here are a few trades that feature various other jumping on points and self-contained stories.
Astonishing X-Men: Gifted - This is the start of Joss Whedon's run on X-Men. It uses Kitty Pryde's, a former X-Man, return as the entry point for a self-contained story told over four volumes (a.k.a. 25 issues).
Captain America: Winter Soldier - Ed Brubaker's Captain America has been critically acclaimed and features probably the best take on the character...ever. This is where it starts. Brubaker took the possibly tired concept of Cap and injected a lot of political intrigue and thriller/crime elements into it.
Runaways - This is one of the few 100% original, 100% new comic books Marvel has put out. It features characters that debut for the first time in this comic, who have no previously existing ties to continuity, and they mostly stay independent of the rest of the Marvel Universe. It's an adventure with new characters in the Marvel Universe, but not tied to it.
The Ultimate Universe was created in the early 2000s to provide new comics for readers to jump into without knowing continuity/only knowing stuff from movies and TV. Of course that was 10 years ago and that universe now has continuity. BUT it all started here, and they do exactly what they set out to do...and do it well.
Lastly, the Marvel Masterworks series collects classic Marvel Comics from the 60s-70s. If you really want to start the story here and actually enjoy reading Silver Age comics, you can start here.
