I don’t think that Doonesbury should be on the editorial page of the newspaper for the same reason I don’t think Dilbert should be in the business section. It marginalizes the audiences for these strips. In the case of Doonesbury, I think it makes the strip feel like it’s not a regular comic, and that you should only read it if you’re well versed in politics.
There seem to be two types of Doonesbury readers: those who follow it every day and those who read it occasionally but get frustrated by the immense number of characters and political angle. I used to fall into the second category…. I thought Doonesbury was way too complicated and I didn’t get the jokes.Then I read all the collections, starting with the very first strip where B.D. meets Mike. Some of the earlier strips were difficult to slog through. I think Garry Trudeau's art has improved more over the years than any other comic strip artist I can think of and the later years are a pleasure to read. But once I read the collections, I finally understood who all the characters were and how they related to each other. Trudeau makes a lot of references to previous events in the characters lives, and the jokes are very funny when you get them.
It's still the only comic strip to have won the Pulitzer prize- which happened in the early years, but I think is more deserved now given the level of reporting and research Trudeau puts into each strip. In 2006 Gene Weingarten did a fabulous in-depth article on Garry Trudeau in the Washington Post which I highly recommend if you have any interest in Doonesbury. I grant that the strip has some inconsistencies and the characters only seem to age every ten years. But overall, it's a great read.
Doonesbury is the only strip that has really dealt with the Iraq war and it is continuing to do so in a poignant and intriguing way. Trudeau has given me an inkling of the anger and healing that happens after an amputation... something you don't see in Garfield every day. Not all subjects are political though. Two years ago, there was a fantastic series on a character applying to college, which was relevant to anyone who's been through the experience.
If you do decide to read the collections, start with the big omnibus editions that contain multiple years. It will give you more consistency than the short books. Go in this order: The Doonesbury Chronicles, Doonesbury's Greatest Hits, The People's Doonesbury, Doonesbury Dossier and Doonesbury Deluxe. There's lots more after that if you're interested (and the artwork gets a lot better) but the first few books should at least give you a good character base. The books mentioned above are readily available in libraries, bargain bins and used bookstores everywhere.
If you do decide to read the old strips, remember that some of the political strips are extremely timely to the period they were written. I feel it's okay to skip them if they're not making you laugh. The point of reading the collections is really to understand the relationships between the characters. Flashbacks: Twenty Five Years of Doonesbury is a great book and is a good place to get a primer and context. If Doonesbury overwhelms and confuses you, give it another chance. Pick up a collection. Start reading the strips regularly. Read the Doonesbury website (which is part of Slate.com). You don't have to know everything about politics to find it funny, I promise.