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I encounter the term motif in composition books, and still have no idea what a motif is. Many sources (including some dictionaries) try to define it as "prominent sequence of notes" or "basic theme of a melody", or even "repeatable part". But hey, after all both brick and window are fundamental elements of a house. So, which one is the building block? Both? I mean, motif and measure and theme and melody are all considered building block of a piece of music. So, how do we can differentiate them?

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A motif could be a melodic or rhythmic fragment. We're not talking about semantic building blocks like meter or harmonic language, but musical building blocks. The immortal example of a large-scale piece built off of a prominent motif is Beethoven's Symphony No. 5 in C Minor.

The first four notes are the rhythmic and melodic motif, which is used compositionally in transposition, inversion, and variation through the entirety of this first movement.

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Also fun is New Horizons in Music Appreciation. –  NReilingh Jul 18 '11 at 19:14
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So, if you give 10 composers a unique song, and ask them to specify motif, do they all come to the same answer? I mean, is motif recognition is composer based, or is it robust enough to have rules and formulas to be found? :) –  Saeed Neamati Jul 19 '11 at 5:25
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For any unique piece of music, most musicians familiar with structural analysis of music will come to the same conclusion. There are plenty of pieces with no recognizable motif whatsoever, but it's a common occurrence in many classical styles. The "rules," like many things in music, are not well-defined; but if you can identify a musical snippet that is self-contained enough to be an idea, and then analyze how that idea is elaborated upon in the remainder of the piece, you're probably safe calling that idea a motif. –  NReilingh Jul 19 '11 at 15:53
    
This is something I can call an answer. Thanks @NReilingh –  Saeed Neamati Jul 19 '11 at 16:03
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A "motif" is a basic sequence of rhythm and/or melody that is used as the "building block" to a "theme", which is a larger overarching musical idea.

NReilingh's example of the first movement of Beethoven's 5th is an excellent example of the use of a motif to create a theme. The four-note motif is an identifiable repeating block within the "theme" that is Beethoven's 5th.

Here's another example, a personal favorite of mine:

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Still not clear to me. Still I have nothing to formulate a motif and differentiate it with theme. Motif is smaller than theme? How to determine? By length? –  Saeed Neamati Jul 19 '11 at 5:28
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Another use of a motif is as a "Leitmotif" ("leading motif") in an opera, associated with a character, thing or idea. It can be long enough to be considered a "theme" but usually it is shorter; sometimes only a few notes or a single chord. Sometimes it is only played once at a time, but sometimes layered on itself or on other music in complex ways.

Some composers of music for animated cartoons used leitmotifs. Carl Stalling did the play-it-once thing in Bugs Bunny cartoons, quoting well-known pieces of music: "Powerhouse" for a factory, "The Lady in Red" when Bugs Bunny dressed up as a woman, etc.

The first Popeye cartoon had an original song, "Popeye the Sailor Man". The theme was used as a motif in all of the rest of the Popeye cartoons. At the beginning it might be heard in a jaunty rhythm as Popeye walks down the street. When he eats spinach, it is played fast and loud by a trio of trumpets, and then during the resolution it becomes a heroic march. This is based directly on techniques pioneered by von Weber, Wagner, and especially Liszt.

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