One perfect example would be the classic rock group ensemble of two guitars, bass and drums. Along with one, two or three members singing, this was a widely used 'standard' ensemble. There were lots of variations, of course. But this ensemble, popularized by the Beatles, was almost ubiquitous.
Some of the variations included using the instrumental group, but adding a singer who didn't play an instrument: this is the Rolling Stones lineup. Another variation is dropping the second guitar: this was the ensemble used by Cream and the Jimi Hendrix Experience. Here is Jimi, showing what a wall of Marshall amps can do:
You could do both: drop the second guitar and the bass, have a singer and add a keyboard: this was the lineup for the Doors (singer, lead guitar, keyboard who also played a bass line, and drums). Or you could have a singer and drop the rhythm guitar giving you singer, lead guitar, bass and drums. This is the lineup for The Who. The basic format lasted a long time and is still used. The Talking Heads consisted originally of two guitars, bass and drums with one of the guitarists as main singer.
At the time of the film Purple Rain, Prince's group consisted of himself as main singer and lead guitar player, rhythm guitar, keyboard, bass and drums.
Another classic ensemble is the piano trio in jazz consisting of piano, string bass and drums. Sometimes another instrument, like a saxophone, is added which allows more prominence to be given to melodic lines. A good example is the Dave Brubeck Quartet. Here they are with the classic "Take Five":
There are also classic ensembles in classical music, of course. If we go back a ways, a classic ensemble during the Renaissance was a group of unaccompanied voices, often used to sing madrigals. Here are five singers performing "Se la dura durezza" by Jacques Arcadelt (1507 - 1568):
Another popular ensemble during the Renaissance was the lute duet:
A classic Baroque ensemble was one or more melodic instruments accompanied by thorough bass or continuo, meaning harpsichord and bass viol or cello. François Couperin's Concerts royaux are classic examples:
A successor to this ensemble was the piano trio of the Classic era: violin, cello and piano.
This late-18th century ensemble lasted well into the 20th century. Here is Shostakovich's trio in E minor, written in 1944:
As you can hear, different composers can do utterly different things with the same ensemble. Now we come to perhaps the most classic of all ensembles: the string quartet. Here is an early example by Haydn who originated the form as something for friends to play together for their own amusement. Here is the finale of op 20 no 5, a little fugue with two subjects:
And skipping over a couple of hundred years of music history, here is what one 20th century composer, George Crumb, did with the form. This is the first part of the quartet Black Angels entitled "Night of the Electric Insects":
I've been focusing on what are usually called "chamber ensembles" but perhaps the greatest of all musical ensembles is the symphony orchestra, whose magnificent panorama of instrumental sound has no real rival. Let's end with what is often called an "orchestral showpiece", part of the finale to The Firebird by Stravinsky: