Hoo. Loads. Personally I play 3 kinds of pipes... Let's see. There's your standard 'Great Highland Bagpipe', which is the one you probably think of when someone says 'bagpipes'. This is mouth-blown and has 3 drones (one bass and two tenor, all tuned to A/B flat) which all attach separately to the bag, and a chanter (the bit the tune comes out of) with 9 notes. There are at least two other Scottish bagpipes; 'border pipes' sound similar to although much quieter than Highland pipes, they are bellows blown (you pump them via a bellows with your right arm) and have three drones, sometimes one bass and two tenor, sometimes one bass, one baritone and one tenor, either all tuned to A or two tuned to A and one to E. The drones are all bunched together in one 'lump' from a common stock and generally sit across the player's chest, not up over the left shoulder. They have a chanter similar to Highland pipes but it allows many more 'sharps and flats'. 'Scottish small pipes' look physically similar to border pipes, but sound an octave lower, and are much much quieter. They have a chnater similar to the others except because its central bore is parallel rather than conical, you can't get any naturals/sharps by cross fingering.

Then you have 'Northumbrian small pipes'. Again they are bellows-blown and have drones issuing from a common stock. They are quite quiet. The chanter is like the Scottish smallpipe one but it has lots of keys, a bit like a flute, to enable a much wider range than any of the Scottish pipes. These pipes have a very distinctive sound, kind of 'pootly' or 'blippy'.

'Uillean pipes' are the Irish pipes you have heard on the soundtrack to Titanic and Braveheart. They are bellows-blown and have a weird highly evolved drone system... the drones sit under the right arm, and are so long they have bends like a trombone slide to keep them a manageable size. There are also 'regulators' which are sort of like keys on the drones that you can press with your right arm while playing to change the pitch of the drones. So Uillean pipers can accompany themselves! Again they have a chanter with keys and have a wide range.

I could go on and list the various European bagpipes but that's probably already way more information than you wanted! :-)