What is delay?
Delay is an effect that records what's played, stores it and plays it back after a certain amount of time. This creates an echo to the original source, so what you play on your guitar is mimicked by a delay pedal which can be set to different time and amount of delay. There are two types of delay: analog and digital. Analog delay uses the old fashioned way, recording your sound on either a tape or a rotating magnetic drum (which endures the test of time much better than a tape, which wears out pretty fast) or on a bucket brigade device. A digital delay takes your signal and passes it on through a series of digital signal processors that records it into a storage buffer and later plays it back, everything set to your parameters.
Any good examples?
Delay must be one of the most used effects in the world of electric guitars so there's of course lots of them. For instance, a lot of old rock songs has the slapback echo (a long delay, somewhere between 75 and 250 milliseconds), especially those produced by Sam Phillips on Sun Records. He noticed that no live sound could ever be heard wihout an echo and therefore he used this effect to add realism to his recordings. The result is a nice sound with much depth which can be heard on a lot of Elvis Presley songs like "Blue Moon Of Kentucky" or "Heartbreak Hotel". Hank Marvin of The Shadows is another player who's famous for this kind of delay, listen to "Peace Pipe" for an example. A more modern example is The Edge of U2, who most people tend to think of when they say delay. He has really integrated the delay into his sound and many of his guitar figures builds around this, listen to "Where The Streets Have No Name" for a distinct example. Delay is also used in classic and hard rock, listen to "Brighton Rock" by Queen or the intro to "Welcome To The Jungle" by Guns N' Roses for conviction. Another classic track, "Every Breath You Take", also features a delay pedal on the guitar played by Andy Sumners of The Police
Which pedal should I get?
To start with the analog choices and a guitar hero, Randy Rhoads relied on the tape-based Roland Space Echo RE-201 (which is not a pedal but a large box). Other choices includes the Boss DM-2, the Aqua Puss Way Huge, Mooer Echolizer and the MXR Carbon Copy. Moving on to digital delays the first foot pedal unit ever produced was the Boss DD-2. Today, pedals like DD-3 and DD-7 (which even has an analog mode, and a backwards effect) is business standards. Other great digital delay pedals are the Strymon Timeline, the Boss RE-20 Space Echo (which digitally modulates an analog Space Echo RE-201), the extremely versatilite TC Electronics Flashback X4, the Strymon El Capistan (which also digitally modulates an analog tape delay) and the Electro-Harmonix Deluxe Memory Man. Also, not so long ago Korg started to make their SDD 3000 as a pedal unit (before it was just a rack effect that was both expensive and hard to find - maybe because The Edge bought them all?). This is a great machine with fantastic delay and more options than you could dream of. The prize? Well, quality costs...