It's been said a couple of times here, but 'the best band of all all time' is purely an individual preference.
Personally, I can't go past Queen.
All 4 members wrote number 1's (no other band in history can claim that), so their song-writing ability is top notch.
Both Freddie Mercury and Brian May are universally recognised as being in the top echelon of their craft (they may not always win the polls of the greatest singer & guitarist respectively, but they're always up there). John Deacon and Roger Taylor were hardly duds at their instruments.
Queen started recording in 1971, and people young and old still love singing along to their songs. Some of their songs include Bohemian Rhapsody (frequently rated the greatest song of all time), We Will Rock You, We Are The Champions, Another One Bites The Dust, Radio Ga Ga, I Want To Break Free, A Kind Of Magic, Crazy Little Thing Called Love, Somebody To Love, Under Pressure, ect.
While Freddie was alive and Queen were touring, it was generally accepted that they were one of the best live bands ever, and were the best at the time. Their record sales were always through the roof. Today, still, Queen's Greatest Hits album is in the top 2 or 3 biggest selling albums of all time world-wide.
I could go on about how they've crossed musical genres in their time (rock, mock-opera, pop, funk, rock-a-billy, soft lovey-dovey music, movie soundtracks, ect), but I won't bore you with that!
PS: 'Queen' (in their new form of just Brian May and Roger Taylor) have been touring again in 2005 for the first time since 1986. They enlisted the help of former Free and Bad Company singer Paul Rodgers to sing with them. Officially, it's billed as Queen+Paul Rodgers. Every concert has been sold out, so they obviously still appeal to people as a live act. The recent release of one of their shows on cd (and soon to be on dvd) called 'Return Of The Champions' is awesome. As Molly Meldrum often says, "Do yourself a favour ..."!