Roland's TR-808 drum machine was released in the early nineteen eighties, at a time when Linn's LM-1 was showing people that drum machines could actually sound realistic. The TR-808 does not sound realistic. Whereas drum machines like the LM-1 store digital samples of drum sounds and faithfully reproduce them in reasonably high fidelity, the TR-808 is an analogue beast, using electronic circuitry to generate from scratch, well, analogues to various drum sounds.
There were two main advantages to this method of generating drum sounds. One was the relatively cheap price: at roughly a thousand US dollars, the TR-808 was a mere fifth of the cost of the LM-1. These days, however, digital sampling is ridiculously cheap, so analogue sound generation no longer has an advantage in that regard. The other advantage was, and still is, the TR-808's versatility. Using its various knobs, you can meticulously adjust, say, the snappiness of its snare drum, or the time it takes its kick drum to decay into silence.
If you want realistic drum sounds, the TR-808 is not for you. It sounds like a piece of electronic equipment, precisely because that's what it is. It does not sound anything at all like an acoustic drum kit. It does, however, sound good in its own right, although it's somewhat an acquired taste and may give you listening fatigue. Its distinctive sound is overall synthetic, weak and unimposing, but its kick drum is close to a pure sine wave. This means that when played on a cheap hi-fi, you can barely hear it, but when played on something that can emphasise bass frequencies, it sounds very, very powerful.
Aside from being used on its own to provide a distinctive, electronic sound, it can also be used to complement and augment more realistic drum sounds to give the kick drum more oomph and power.
Not only has it been used on many seminal albums (as well as countless bad ones), but it's also an integral part of the electro, techno and hip hop themselves. Appropriately, several rappers and even pop stars have paid homage to it in their lyrics, with Manchester based electronic group 808 State even going as far as to name their entire band after the device.
Due to the ubiquity of its sound and how often it's namechecked by rappers, it's still highly sought after and hence has a second hand price that's roughly equivalent to its original cost thirty years ago. For this reason, along with its unwieldy stature and predating of modern standards such as MIDI that might actually allow it to talk to the rest of a studio, these days people mostly emulate it via clones and samples, rather than actually using the original machine itself.
Songs predominantly featuring the TR-808