So you're not wrong, obviously, in saying that it's hard in superhero comics to find something that doesn't tie into a ton of other books (I can't speak much for DC since I don't know as much over there but I know I was turned off of BATMAN for exactly that reason, though that book was pretty solid. I also hear good things about RED SONJA, but we're getting off-topic already). If it is an ongoing superhero comic you're looking for, I have several recommendations, though obviously it depends on what you like to read.
HAWKEYE is one of the best series I've ever read and stays really self-contained for a book about a guy who has only ever been viewed in context of Avengers teams. It's not a prototypical superhero book (Hawkeye himself appears in a Santa hat for more panels than in his actual costume) so if you're looking for a little more action, this one may be a little slower.
While we're talking about solo titles, BLACK WIDOW and ELEKTRA are both really impressive right now and are staying fairly self-contained (BLACK WIDOW just had a very small crossover with PUNISHER, which has also been good, but you certainly don't need to read the PUNISHER issue to get the full feel for it). BLACK WIDOW has a really strong narrative and outstanding art. It's featured other characters in bit roles here and there but nothing aside from the slight PUNISHER crossover that requires other reading. ELEKTRA is fairly new but it also has great art and a really interesting and dark story.
DAREDEVIL is another good one that has been good for some time now (it's very recently tied in to the Marvel event ORIGINAL SIN but it's not a tie-in that requires you to know more than the very basic outline of the event). Mark Waid and Chris Samnee have taken a character who has been more than a little dark and brooding since Frank Miller and made him a little more fun, kind of more classic DAREDEVIL but with a Miller darkness at the edges. It just renumbered to give fans a jumping-on point so it's only on issue four or five, though this creative team has been working with the character for a couple years now. CAPTAIN AMERICA too has been very strong and kept itself as contained as a major character like Cap can.
As a matter of fact, most solo titles, while I'm thinking about it, are keeping relatively to themselves. The X-MEN books are a little more interconnected (though Si Spurrier's new X-FORCE has already been phenomenal through seven issues and is worth checking out if you like a bit of a heady run mixed with a bunch of asterisk's-out swears; Spurrier wrote X-MEN LEGACY recently and it was my favorite book last year) and some of the main AVENGERS titles have been bouncing in and out with one another (though NEW AVENGERS has more or less kept to itself since INFINITY, last year's event, and that book has been great since the start). There are definitely more Marvel books I'd be happy to recommend but I'm inexplicably already at something like nineteen paragraphs and I haven't even gotten what I'm slowly getting around to.
The worry that a book you like will tie in to a bigger universe is certainly not irrational but it's something you don't really have to worry about with books from, say, Image. I've been reading a handful of those books recently and there are certainly some great ones worth looking into if it's your thing (though they do tend to be a bit more explicit because, I suppose, they can be). SAGA is pretty fun and interesting and it wins Eisner after Eisner, though I personally think it's a little overrated. VELVET and LAZARUS are both really good and pretty new books. VELVET (from Ed Brubaker and Steve Epting, the guys who created the Winter Soldier storyline in CAPTAIN AMERICA) focuses on a spy who has been accused of killing her department's best spy (Brubaker pitches it as "if Moneypenny was accused of killing James Bond"). LAZARUS is about a dystopian future where America is divided up between the richest families while the rest of the world lives in a really regimented caste system. Each family has a programmed warrior to defend them, called a Lazarus, a member of the family who has been genetically augmented and trained to keep his or her family protected and the series focuses on Forever Carlyle, the Lazarus of the powerful and corrupt Carlyle family.
While we're talking about dystopian futures, Jonathan Hickman's EAST OF WEST might be the best comic I've ever read. It's certainly in contention and it's just fourteen issues or so in. The conceit of the book is that there was a giant meteor that struck the dead-center of America in the middle of the Civil War, putting an end to the fighting but also leading to the formation of several separate nations within America. At the same time, a prophecy about the end of the world emerged from a few different sources. Now, centuries later, the nations of America stand on the precipice of war while a handful of zealots sit atop each nation and meet in secret to discuss The Message. If that weren't enough, the driving storyline is about Death falling out with the three other Horsemen of the Apocalypse. It's got a lot of really great art in it and Hickman's writing is really detailed, cool, and smart. I've read that he plans out his arcs in two year blocks, which is pretty crazy in and of itself. Look, it's a really great book, but only, I would think, if the heady plot is your kind of thing.
FINAL PSEUDO-RECOMMENDATION: Ryan North and Boom! Comics just finished an eight-issue run on an original series called THE MIDAS FLESH that explores the myth of King Midas and what its effects on a world/universe would be. I love North, who writes the very funny webcomic Dinosaur Comics, and his humor and interesting scientific questions are all on display in this series. Lots of fun in this series based on an idea in one of his Dinosaur Comics though it did just end, so not a ton of longevity on that one.
