Even if it can seem like a real "singer tune", lots of instrumentalists play this tune simply for the fun of improvising on it. Its 32-bar structure (very straight-forward) and it's ABAC form make it a good candidate for soloing. Usually, the tempo is med-slow and, to my knowledge, always played with straight eighth-notes.
Lots of jazz player appreciate this piece because it's a nice "latin feel" not-too-fast ... and not-to-dark type of form! It has *some* darkness, and a nice balance of brighter progressions. Starting of in what seems to be Em, we quickly hear the G major tonality... then the B part is quite minor with consectuive MINOR II-V cadences. The repeated A section brings back a sense of freshness and the "climax" is finally attained at 3/4 through the form, like most timeless pieces.
All in all, we can say that this tune is pretty much in E minor / G major with some interesting detours. You may find it challenging to improvise on the B and C sections of The Shadow of Your Smile : take your time. Learn the chords, learn the scales and see how it all fits together in the big picture.
Please see the Podcast #7 on JazzGuitarLessons.net for a complete harmonic analysis and some ideas on blowing.
The only version I particularly enjoy listening to is Astroud Gilberto's. You can find countless versions on Youtube and Itunes I'm sure, but I've personally never bothered to seek them! (-:
Suggested listening :