The American newspaper comic strip is in many ways a unique and fascinating medium. Much fine work has been produced in this form over the years and it is a genre well worth exploring. Here are some places to start.
The Essential Collections Smithsonian Collection of Newspaper Comics is probably the best single collection out there. Blackbeard and Williams did a fine job collecting and introducing and the reproductions are excellent. The collection covers the 1890's through 1950's well with only a smattering of later strips. This is the best place to start for a general overview. It includes a good sampling of Little Nemo, Krazy Kat, Polly and Her Pals as well as a healthy selection of Popeye, Alley-Oop and Gasoline Alley (including a wonderful tour through modern art "from the inside"). (Tip: search on "Smithsonian Newspaper Comics" as there are several editions out there which may be cheaper)
They followed up with "The Comic Strip Century" which has been reprinted as 100 Years of Comic Strips with a rather garish and ugly cover. As it's a follow-up to the Smithsonian volume above, there is no overlap and makes a great supplement - it's all the stuff they couldn't fit into the other book, but wanted to.
Brian Walker's two collections The Comics: Before 1945 and The Comics: Since 1945 (now available in a single volume The Comics: The Complete Collection) offer generous helpings of comics and some decent commentary. A minor theme throughout these two books is strips that relate to the comics medium itself, such as a Family Circus strip in which Grandma recalls the comic characters of her youth (Happy Hooligan, Krazy Kat, Mutt and Jeff, etc.) while Billy is thinking of modern strips (Peanuts, Garfield, etc.). This gives these books added depth in that the comics are commenting on each other and their place in our lives. There is very little overlap with the volumes above and the choice of strips is very fine. Being more interested in the earlier strips, I have a greater fondness for The Comics: Before 1945, but that's just me.
Masters of American Comics is a lovely book focusing on a handful of artists and reprinting a good deal of work. The text (essays by a number of different authors) varies greatly in quality. This book accompanies a museum exhibition designed to elevate these artists into the canon of fine art.
Single Strip Collections I can't list everything here, so I'll just list some of my favorites and things I consider essential.
Krazy Kat - My favorite, my son's favorite, the critic's favorite - you can't get away from Herriman's Krazy Kat. Admittedly some people just don't get it. It's oblique, strange, nonsensical and repetetive. Even when it appears to be plot-driven, it usually isn't. Personally, I find that in reading Krazy Kat, it takes me four or five strips to get into the rhythm and to re-enter Coconino County, but once I'm there the joys are plentiful. There is something about Herriman's seemingly endless variations on the "mouse-hits-cat-with-brick-and-gets-thrown-in-jail-by-dog" theme that gives these strips a timeless quality (and one can see a modern equivalent in Chris Ware's work - it's no coincidence that he's designing the covers for Fantagraphics). Fantagraphics has reprinted all the Sunday strips starting with Krazy & Ignatz 1925-1926: "There Is a Heppy Lend Fur Fur Awa-a-ay" (Krazy & Ignatz) and continuing. The color strips start with Krazy & Ignatz: Komplete 1935-1936 A Wild Warmth of Chromatic Gravy. This series picked up where the old Turtle Island/Eclipse series left off Geo. Herriman's Krazy and Ignatz: The Komplete Kat Komics, Vol. 1, 1916 and now they've gone back and reprinted the early years as well, so the entire run of Krazy Kat is currently available. You can get some collections of the Krazy Kat daily strips like this one Krazy & Ignatz, The Dailies. Vol 1. 1918 -1919 and others (search the internet for the Pacific Comics Club series) but they are of less interest than the Sunday strips. A good overview and bio is also available: Krazy Kat: The Comic Art of George Herriman which reprints lots of strips (Sunday and daily) from across many years.
Gasoline Alley - a very sweet and gentle strip currently being reprinted in Walt and Skeezix: Book One, 1921 & 1922 (Walt & Skeezix) (Bk. 1) and subsequent volumes. This is an extremely long-form "graphic novel" telling the life stories of its characters over decades. The notable feature of the strip is that the characters aged in real time so that the baby Skeezix becomes a boy, a teen, a young man, an adult as Walt moves from young adult into middle-age and beyond. The Sunday strips were generally not part of the continuing story line and often emphasized graphic artistry. Drawn & Quarterly (Volume 3) has some wonderful Gasoline Alley Sunday pages. Really some very fine stuff with innovative art.