If you have played more than one or two jam sessions, then you have played this tune.  "Almost Like Being in Love" is one of the most popular, heavily played standards.  But I bet you have not played it like this before.
This is a fast-moving jazz-rock 6/8 style.  This is good practice for adjusting a melody to fit a different beat pattern.  The chord changes move quickly in this high-energy style.
This track begins with an 18-bar intro -- hey, it doesn't always have to be 4 or 8.  The song form is AABA with the AAB sections each being 8 bars.  The final A has an extension that makes it 12 bars.  After the final chorus, we fall into an 8-bar vamp for open soloing, if only that %$%#$ guitar would turn down a little.  :)

Ready for something a little easier?  Sonny Rollins popularized the tune "St. Tomas", which is actually an ancient folk melody. 
Normally heard as a calypso tune, we will practice it in a samba style, which is similar, but maybe easier to feel the beats.  Samba is a solid 2-beat, usually with heavy syncopation.
St. Thomas is a simple melody of just 16 bars.  The first 4 bars (as well as the next 4 bars) are all in the C major key center, with the pattern:
                            |   I        |   iii     VI   |    ii    V   |   I         ||
The only chord in that entire sequence that departs from the C major scale is the third chord which is VI (major) instead of the normal vi (minor.)  In other words, that one chord wants a C#.  So basically you can play the first 8 bars using notes from the C major scale.  If you happen to play a C natural on that third chord, it becomes A7(#9) which is plenty cool.
The last 8 bars depart from the C key center a little, but if you play with an "island spirit" nobody will complain if you don't venture beyond the C major notes.
You can simplify even more if you like.  You can think like a steel drum that may have only 3 or 4 notes available.  You can make a hip-sounding solo just playing some combination of C, E, and G.  It doesn't have to be complicated to be fun.

And here's the same thing in a "soul calypso" style.  A conventional calypso is a rather straight beat.  This "soul calypso" has the spirit of the calypso, but a little bit of funk for good measure.  It is driven by a 2-3 clave throughout.

This Bill Evans song follows the tradition of other waltzes like My favorite Things and Bluesette by using an extended song form.  That is the biggest challenge with this song.  I would call it AABAC, with each of those sections being 16 bars. 
In the A sections, the chords are inverted more often than not, with the bass playing the 3rd, 5th, or 7th instead of the root.  This inversionthe song more of a "Broadway musical" sound than cool jazz.  Of course when Bill Evans played it, there was never any question a jazz master was at the keyboard. 
The bass line in the A section is real genius as it moves downward chromatically in a truly elegant way.  Musicologists refer to this as "suspended tonality."  But the soloist must not be distracted by that.  You won't find the tonality in the bass during these passages and you might not hear the roots clearly in the other instruments.  The chords themselves are not terribly exotic.  You just have to learn the chords and appreciate that the bass is adding a completely different quality at those moments.
In the bridge, the bass is on the roots throughout and in the final 16, the bass has a few measures lingering on a pedal C, giving it a more conventional jazz sound.
Evans often played this song as a rubato waltz for one chorus, then went into a swinging 4.  For this practice track, we stay in jazz waltz throughout.  The last time, the final phrase is tagged twice.

Here is a tune very few players know.  You are unlikely to hear this one called up at a jam session. This Art Blakey tune is worth learning because it it so original and clever in its composition -- plus it is just plain fun.
It is a jazz waltz, but played faster than anybody could waltz to.  It almost comes across as a conventional 32-bar ABAB song.  But instead it pulls up after 30 bars, and tags an 8-bar modal section on G7sus4.
The changes are interesting.  Except for the 8-bar tag, the changes are always one chord per measure.  And with the tune moving at quarter=170, these chords come quickly and give it a strong pulse.  The chords in the A section have a bluesy feel, but what is unusual about this song is a pattern of 3 "normal" chords followed by a surprisingly strong chord in the 4th and 8th bars of the each section. This gives the song a feeling almost like the traditional New Orleans "Big 4" beat.
One wonders if the title of the tune was meant to signify 3 sweet chords followed by one sour chord.
The changes (in Dm concert) are:

A:      Dm7  |  G7       |  Dm7  |  Ab7(#11)  |  Gm7       |  C7           |  Gm7  |  G7(#5)  |
B:      Cm7  |  F7(b9)  |  Fm7  |  Bb7(b9)    |  Ebmaj7  |  Abmaj7  |  Gm7  |  A7(#5)  |
A:      Dm7  |  G7       |  Dm7  |  Ab7(#11)  |  Gm7       |  C7           |  Gm7  |  G7(#5)  |
B:      Cm7  |  F7(b9)  |  Fm7  |  Bb7(b9)    |  Emaj7    |  A7(#5)    | 
Tag:   G7sus4 for 8 bars

Alec Wilder is not as well known as, say Richard Rodgers or Cole Porter, but he wrote some of the best melodies ever.  I'll Be Around is a perfect example of a timeless tune that can be done in many styles. 
Nothing too complicated here.  Simple 32-bar AABA form and remains in the concert C key center throughout.
This one is a modern straight-8 pop ballad style.

This Stanley Turrentine tune is a favorite at jam sessions.  Nothing too complicated here, but you do need to take the time to learn all the changes as they cover a lot of ground, particularly the back half of each chorus.

This Todd Dameron cutie is well worth learning.  It is only 16 bars, but don't be deceived.  It has twists and turns at every measure.  When one listens to the song, it seems simple enough, but when you try to play it you may find the changes don't go where you thought they might.  That's the mark of a very clever composition.

This is a crooner's favorite, but it can be a good canvas for any instrumentalist as well.  The song form is a little unusual.  It is an AABA form, but the A sections are 6 bars each, then the last A has a 2-bar tag, haling that line 8 bars, so the total chorus is 28 bars.  Sometimes people leave off that tag, making it a 6 + 6 + 8 + 6 = 26-bar chorus.

The changes are all rather ordinary.  The A section has that I - vi - ii - V7 pattern we see so often.  The B section has 11 - V - I - VI twice in G and then the same thing twice in Ab, which is why we practice our scales in every key.

The real selling point of this song is its lyrics, so an instrumentalist should keep those lyrics in mind while soloing:
A: Pennies in a stream, Falling leaves of a sycamore, Moonlight in Vermont.
A: Icy finger waves, Ski trails on a mountain side, Snowlight in Vermont.
B: (key of G): Telegraph cables, they sing down the highway and travel each bend in the road.
B: (key of Ab): People who meet, in this romantic setting Are so hypnotized by the lovely...
A: Evening summer breeze, Warbling of a meadowlark, Moonlight in Vermont.
Tag: You and I and Moonlight in Vermont

A great ballad standard, "My Old Flame".  The song form is a straightforward 32-bar AABA.  This one is set to a modern pop ballad style with a strong straight beat.

Here's a tune that everybody should know.  Frenesi is played in a variety of styles, often bossa or bolero.  This is a cha-cha style.  But beware, this is a Cuban cha-cha!  The bass is probably not where you expect it.  Cubans often move the bass notes ahead by a half beat.
The song itself is not complicated.  It is a 32-bar AABA.  The main tune is in Ab concert.  The bridge is up a major third to C.