Nothing encompasses colorful spectacle and British pageantry more than the Changing the Guard ceremony at Buckingham Palace.
Foot Guards have stood guard at St. James Palace since 1660.  When Queen Victoria moved into Buckingham Palace in 1837, the Queen’s Guard remained at St James’s Palace, with a detachment also guarding Buckingham Palace, as it still does today.
Each guard stands at post for 2 hours at a time with every 10 minutes marching 15 paces 5 times.  Don’t be fooled!  The Queen’s Guard are highly-trained, operational-duty soldiers armed with functional firearms loaded with live ammunition.
The Changing the Guard ceremony is 1.5 hours long and is accompanied by the Guards marching band. The music played ranges from traditional military marches to songs from films and musicals and even familiar pop songs.
It is not possible to stand in one place and see all of the ceremony as it is a multi-step ceremony with activities taking place in several areas at the same time and there is a lot of coming and going between the two palaces and detachments arriving and leaving.  In fact, in between the arrivals and departures of the different detachments, car and pedestrian traffic resumes on the streets in front of Buckingham Palace.  It was during one of these breaks that the people in front of me thought the ceremony was finished and left so I was able to move right in front and see without any obstruction.
If you enjoy watching marching bands than it is best to stand just inside Australia Gate on Spur Road looking towards Buckingham Palace.  This way you can see the marching band and the old and new detachments arrive and leave.

If you would prefer to watch the actual handover ceremony than it is best to arrive early and stand outside the fence in front of Buckingham Palace.  You won’t see very much of the arrivals and departures, but you will see all of the actual ceremony that takes place inside the palace gates between the old and new detachments.
At the same time that the Changing the Guard ceremony is being performed, there is also the Horse Guard Parade.  The Queen’s Life Guard have stood guard at Horse Guard, the official entrance to the St. James and Buckingham Palaces, since 1660.  These are horse-mounted guards.  When the Life Guards change from the Old Guard to the New (relief) Guard, they ride past Buckingham Palace on beautifully groomed horses with breastplates that shine in the sun.  It is breathtaking and you think you have been transported back into medieval times with knights in shining armor.
A.A. Milne, the creator of Winnie-the-Pooh, wrote a poem about Changing the Guard called Buckingham Palace.  One of the stanzas reads (italics mine):
They’re changing guard at Buckingham Palace –
Christopher Robin went down with Alice.
A face looked out, but it wasn’t the King’s (Queen’s).
(S)He’s much too busy a-signing things,”
Says Alice.