appreciation day, one of the few things that S&W Complete didn't use from the OD&D supplements that I'd actually want in a game was the artifacts from Eldritch Wizardry. For me, artifacts were always an excellent part of the shared mythology of Dungeons & Dragons; having started with the 1991 set and gone on to AD&D 2e, the artifacts were the most colorful and interesting parts of the DMG. Of course it told you basically not to use them, which meant that in my earliest games I wanted to use them. Later when I got involved in online communities they provided one of the touchstones of stuff that every gamer knew and shared in some way. Even today you should recognize that the picture for this post is the Hand of Vecna.
One of the important things that artifacts provided for the game was the creation of the illusion that the world has a rich history behind it even if it doesn't. Not every fantasy world should require the depth of imagined material as Glorantha or Tékumel or Middle-Earth, Hârn or the Forgotten Realms. As much as I love reading fantasy setting material, I think worlds with sketchier backgrounds are better for some kinds of gaming when not everybody needs a strong familiarity with years (in many cases, now decades) of intricate detail.
In some cases, less is more. I don't know what a wind Duke is, or where and what Aaqa is, but the Wind Dukes of Aaqa that I invented in my head on hearing the name are cooler than the ones detailed out in the late '90s by Wizards of the Coast employees. Just like the Clone Wars I imagined as a kid are better than any media adaptation of them from 2002 onward. It takes a master storyteller to get something legendary really right, and having a mediocre version is sometimes worse than having a vague legend that you fill in yourself.
I like artifacts in a couple of other, more game-related senses. First, they transcend the concept of the "typical" magic item and become special because of their uniqueness. The fact that a good artifact should have at least some downside really reinforces this: magic is something special, not a sort of technology. Second, they are good for higher-level play, giving a viable goal aside from gaining levels and getting treasure. Since they are legendary, they let characters connect and become legends of their own through their deeds - rather than just rich and possibly famous.
Exactly what artifacts are has been discussed before; relics are kind of an odd subject. Of course "relics" are physical pieces of saints, such as bones, teeth and hair. For instance, Roland's sword Durendal was supposed to have a tooth, blood and some hair from various saints as well as a piece of the Virgin Mary's garments in its hilt. Such things can give mystery to an artifact, but not necessarily act as one itself, unless like Vecna's hand it's a whole body part. (At this point I would be remiss not to link to the Head of Vecna.)
One question on artifacts that's interesting to me is the way they are presented in the AD&D 1e Dungeon Master's Guide. Each artifact is presented with a number of power "slots" for the referee to fill out on their own. In a way I like this, since it means that artifact powers remain a mystery even to players who have the books. That can be a hard thing to do, although it does strip out some flavor. I'd probably prefer a hybrid solution, with some "set" powers and some "open" powers, so that the artifacts retain their mystery but have flavor appropriate abilities and drawbacks. It certainly beats the way magic items ended up in later editions.
So I think some artifacts will be part of Dungeon Crawl #3. If there is enough interest over time, I'd like to put out a whole booklet full of the things, complete with new tables and rules for artifact powers. It seems like they're just a missing part of the OSR field at this point.