What is a phaser?
A phaser effect is produced when the guitar signal is split in two signals, one of them is altered by a filter which creates peaks and notches in the phasing spectrum. This signal is mixed together with the original signal, which results in two signals that are out of phase with each other and the notches that occurs gives the characteristic phase effect. A flanger is a similar effect, the difference is that a flanger delays the altered signal where the phaser does not.
Any good examples?
There are many different examples, for instance the phaser played a big part in Eddie Van Halen´s "brown sound", which ca be heard on tracks like "Atomic Punk" and "Eruption". A very different guitarist that uses the phaser in many songs is Radiohead´s Johnny Greenwood, listen for example to "Paranoid Android" for it. Classic Rock guitarists Brian May of Queen and Jimmy Page of Led Zeppelin likes to emulate their sound with a phaser, listen to "We WIll Rock You" and "Ten Years Gone" for good examples. A modern alternativa band that likes to use a phaser is Tame Impala, you can hear it on tracks like "Solitude Is Bliss". Nu-metal act P.O.D. and alternative rockers Incubus are also fond of the phaser effect and uses it everywhere, Incubus even has a song fittingly named "Just A Phase".
Which pedal should I get?
To begin with the classics, the EHX Small Stone is a great pedal, so is the MXR Phase-90. The first one is used by Johnny Greenwood and Korn guitarist Munky, the latter has fans like Tom Morello (Rage Against The Machine, Audioslave), Dave Grohl (Foo Fighters) and John Frusciante (Red Hot Chili Peppers). But there are other choices too, like the versatile Boss PH-3, the Digitech Hardwire SP-7, the T-Rex Tonebug Phaser or the Epress Effects Phaser Pedal. From one knob to five, the choice is yours. Remember that sometimes simplicity is best, but not always, it all comes down to your taste.