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One of my Facebook friends posted this sheet 
I was shocked by the quantity of clefs being used. Moreover, they aren't placed at the same vertical position (which I assume changes the reference points for the notes after that).
Is it common practice to use that many different keys on different vertical positions ? Or is it just an extreme example to serve as academic purposes ?
Switching clefs is not uncommon. It can provide notational convenience when a part shifts to a higher or lower range than the current clef easily encompasses. However, the piece you've posted is an exercise in reading clefs and quickly shifting between them. It's highly unusual, but useful for training as a conductor, for example, where switching from clef to clef within the various parts of a score is necessary.
As an aside, here's a Wikipedia note on the composer.
Example 1: Reading as a conductor
Here's a typical, uncomplicated example of the demand made on a conductor. There are three different clefs to be scanned. (The excerpt is from Tchaikovsky's Sixth Symphony and begins in the first movement, seven bars after rehearsal A in the linked score.)
Note that the treble-clef instruments are notated in different keys, because of the instruments involved. So not only does a conductor need to clef-switch, but must also transpose within a clef.
Example 2: Notational convenience
Compare these two editions of Chopin's Etude in A minor, Op. 25 No. 11. Both images are of measure 11.
This first image comes from the Pachmann edition. Note that the pitches are written in their canonical staff positions.
Contrast this with the Paderewski edition, in which the highest notes in both staves are altered: the right-hand (upper) staff with an ottava, and left-hand (lower) staff by a temporary change of clef from bass to treble and back.
The sheet music you posted is a solfege exercise, that's why it contains all those clef changes.
(etude de solfege = study of solfege = solfege exercise)
And note that there are not only clef changes, but also time signature changes all over the place. Again, it's an exercise.
In actual practice, clef changes are not frequent, but can be found occasionally.
For example, if there's a part in treble clef, and at some point there's a long section with low notes, it makes sense to use the bass clef for that section, and then return to the treble clef afterwards.
As noted, this piece is an exercise designed to help students learn to switch between clefs with ease. For "real" music, here's what Elaine Gould has to say in "Behind Bars" (a common reference for music notation):
For performance material, stay in one clef for as long as is practicable, using up to at least three ledger lines rather than changing clef frequently. This shows the contour of the pitches, which a change of clef would obscure.
This said, it is not always "practicable" to stay in a single clef. Clef changes are most frequently found in parts written for instruments in the alto to tenor range. Among orchestral instruments this includes viola, cello, trombone, bassoon, and occasionally French horn.
Depends what you mean by common, but yes clef changes are common.
It seems to me clef changes were more common in the past. When I compare various pkeyboard editions of music at IMSLP.org it seems older editions that use clef changes where a newer edition will apparently avoid them. I particularly notice a modern avoidance of C clef.
In an exercise I wouldn't all it an "academic" purpose. It serves to learn how to sight read better which is a practical purpose. The more you sight read by relative interval changes - instead of memorizing letters for lines and spaces - the better your reading becomes. If you can do that very well, the clef changes shouldn't be so difficult.
You should notice that in this piece the clef changes are matched with melodic motifs. Notice how the opening in 7/8 is a one-bar idea repeated four times. Each one has a clef change. Think of the clef changes as a kind of signal to transpose the motif.
"Common" requires some criterion like "as often as not". I would not say it's common but it does happen. It is an accepted regular practice. I can cite an example right now, the sheet music for Papagena/Papageno that I am working from has the soprano and tenor on the same line in the beginning, switching back and forth rapidly. This is probably because the melodic call and response is so quick when they start singing "Pa", "Pa Pa", etc. mirroring each other. As soon as the lines get longer and words appear the staff is split and each vocalist gets their own clef.
Another example might be instruments that are in the mid range and have an extended range either into the treble or bass register. Viola or cello comes to mind. I have seen such things in classical scores but they are usually once in a blue moon. In the example you have shown it's everywhere. That kind of makes me think it was written as an exercise for sight reading with rapid clef changes. I don't see any actual key changes. It looks like the key of G maj all the way through. Are you sure that there is a key change?
In musical scores the key can change every measure (a real nightmare). This is usually when every character is singing and each has its own "theme" and key to distinguish it from the others. Fun all around.
This is very easy for reading, you have just to imagine that these are all different pieces of only one measure. (The same like you have always to notice in which clef a sheet music is written!) Then you can be proud that you have learnt so many pieces in such a short time.
Supposed you have no problem to read treble and bass clef, all other clefs are all the same clef: This is the C- clef, that tells you where the middle C is notated. As you are able to read treble clef you just have to mind the notes of the triad on the lines above the middle C are CEG and those in the space are DFA, and the triad from the middle C is the F chord (on the lines) CAF downwards - the notes between the lines are BGE. Now, whats the problem???
Yes, it is common to mix multiple clefs on the same sheet, but the particular example you give is unusual in how much it does it. As others have said, it is probably an exercise in clef-reading and adjusting to changed clefs.
