All the newspapers are calling him "postmodern," which is true in kind of a chronological way, but he really didn't fit that whole ironic life-is-just-a-game-without-rules mold of the postmodern. More than any other modern writer (not that I know that much about modern writing), he tried to meld a contemporary sensibility with a commitment to values, or at least value-seeking, that is universal.
This old interview at Salon, after Infinite Jest came out, has a lot of insights. Some excerpts:
There's something particularly sad about [living in America today], something that doesn't have very much to do with physical circumstances, or the economy, or any of the stuff that gets talked about in the news. It's more like a stomach-level sadness. I see it in myself and my friends in different ways. It manifests itself as a kind of lostness. Whether it's unique to our generation I really don't know.
... I get the feeling that a lot of us, privileged Americans, as we enter our early 30s, have to find a way to put away childish things and confront stuff about spirituality and values. Probably the AA model isn't the only way to do it, but it seems to me to be one of the more vigorous.
... The idea that something so simple and, really, so aesthetically uninteresting [as not lying] -- which for me meant you pass over it for the interesting, complex stuff -- can actually be nourishing in a way that arch, meta, ironic, pomo stuff can't, that seems to me to be important. That seems to me like something our generation needs to feel.
There are certain contemporary writers or artists that one feels like are companions for the journey, and this is different than liking the old writers who are great and nourishing but dead long ago. They (the companions) make one feel not alone. And now DFW has gone, and we're a bit more alone than we were.
One last thing: his essays in books like Consider the Lobster and A Supposedly Fun Thing I'll Never Do Again, are just incredibly funny. His description of the McCain 2000 campaign in Lobster (as well as his evisceration of John Updike in the same) just have to be read. Honor a great writer and go read 'em.