Once upon a time, there was a company called Amp Research (actually, they're still around, but it starts better if I start the story like this). An employee of Amp Research, Horst Leitner, decided that a good idea for a full suspension bicycle would be to have a four-bar design (the wheel is attached to two bars and those two bars to the main frame). His design was relatively simple and used a pivot right in front of the wheel dropout on the chainstay. It became known as the Horst-link. He patented his ridiculously simple but fairly discovered idea because that's what Amp Research is in the business to do.
Specialized ended up buying the patent to the Horst-link. Using the legal system and their newly acquired patent they decided to sue everyone. So, sooner or later, most Horst link designs ended up disappearing. A couple still remain, either as not-so-Horsty looking designs (Rocky Mountain ETSX), legally licensed (but paying Specialized, such as Titus as of now and Giant until 2005), the enigma that is Ellsworth (does anyone know if they're actually licensing the Horst-link?), or outside of the USA (their patent was only ever issued in the USA; see Scott's Genius or Devinci's bikes or other Horsty non-USA designs).
In recent years (since Specialized became particularly evil about their patent and licensing it) many good alternative designs have arrived on the market. VPP (Santa Cruz, Intense), DW-Link (Iron Horse, Ibis, Independent and maybe semi-legally but not officially by BMC), Maestro (Giant, kind-of a DW-Link knockoff, but still a good one), and more are coming. Just see Banshee, Cove, and Haro's new designs.
What these designs share in common with Specialized's Horst-link design is that they seperate the wheel by two links. So, you could call them 'real' four-bar designs. They specifically lack the pivot directly in front of the dropout.
Many other companies took their four-bar design and moved the pivot to the chainstay (above the dropout instead of beside it). Because of this design decision, the wheel is directly connected to the main frame by a pivot instead of a link at the chainstay. There are two other links, but they are effectively redundant and do not do the same thing as the two seperate links in a real four-bar design. See Turner for a saddening story about four-bar gone "faux bar"; also known as a linkage driven single effective pivot (see the Astrix Motolink designs or many Foes bikes for truly linkage driven single pivots). (However, Turner's designs are not specifically worse for this change, see the next paragraph.) Other faux-bar designs exist that don't look Horsty at all; such as the new '06 Rocky Mountain Slayer (yes, it's hard to see at first).
Many people think that the wheel path is what's important in a suspension design, but that's just the beginning of story. Wheel path, chain lengthing, chain torque, compression ratio and rate, braking torque and other factors come into play. While Specialized touts its wheel path as the key results of its Horst-link, it's really the minimized braking torque that is relatively good because of its Horst-link. Other suspension designs can recreate or create better the other factors relatively easy (especially with the ever common platform shocks available in recent years). I haven't even brought up the ease of many designs to be more or less durable and easily maintained based on the locations of their pivots.
(Don't think I'm as anti-Specialized as I tried to sound. They make good bikes, and their ruthless patent enforcement has spurred many great full suspension designs to fruition. I'm mostly anti-patents really.)
Anyway, I kind of lost my target in that speech. So, I'm done now