It's not really what I describe as a band, more like a group of artificial voice synthesisers.
There are many Vocaloids and Utauloids.
The vocaloids with the biggest fanbases are:
link
link
link
link
link (Gakupo Kamui)
link
And
link (GUMI)
There are fanmade Vocaloids that have gotten popular as well, like:
link
and
link.
There UTAUloids such as
link (Who was originally supposed to be an April fools joke and later became an UTAU)
Considering each 'member' is artificial, they are put into many different situations during different songs (made by many different people using the software) And their personalities and over all persona will change depending on what video they are in. Take Rin and Len Kagamine, for example. In certain videos, they are casted as Brother and sister, while in others, they are lovers, or mirror images.