When we say "Time After Time", most people will immediately think of the big Cyndi Lauper hit.  After all, even Miles covered that tune, and it is a good one.
But 6 years before Lauper was even born, Sammy Cahn and Jule Styne collaborated to create a great ballad by the same name.  They wrote it for Frank Sinatra, but it has been covered by musicians from Chet Baker to Rod Stewart.  Although it isn't played as much as some tunes in the America Songbook, it is well worth learning.
It is a familiar ABAB form in 32 bars.  The chords aren't too treacherous, with the A section working the familiar soda pop progression of I-vi-ii-V.  This arrangement has some harmonic substitutions to give it more interest as a jazz ballad.

And here is the original Sinatra version.

No matter how much you enjoy swing and bebop, most players have to be able to play in other styles.  Here is a tune that was a big top-40 hit.  It isn't thought of as an "American Song Book" standard, but it is as worthy as any other tune in the book.  This is Neil Sedaka's brilliantly crafted "Laughter in the Rain".  It has strong lyrics, a very memorable melody and interesting harmonies.

This arrangement is a pop-funk style, so the soloist shouldn't approach it the same way one might go after "Bye Bye Blackbird" or "Indiana".  It might be worth listening to the Saturday Night Live band.  They often play grooves like this.  Generally the solos have fewer notes, allowing more time to develop emotion with timbre rather than a blizzard of notes.

The song is not terribly complicated.  It consists of three main parts.  After a catchy 4-bar intro, there is an 8-bar verse with simple chords in F major concert.  There is a 3-bar interlude ("I feel the warmth of her hand in mine.")  That takes us to the refrain ("Oh, I hear laughter in the rain. Walking hand in hand with the one I love. ...")  But Sedaka cleverly puts the refrain in a completely different key center (Ab major concert.)  The refrain is usually played as a 9-bar section (a one-bar extension to the last chord.)

In this arrangement the pattern is:
  Intro
    Verse - Interlude - Refrain
    Verse - Interlude - Refrain
    Verse - Interlude - Refrain
    etc.
 Intro played again to end.

It is also typical to simply repeat the refrain ad lib for the solos.  In that case, that is usually played as a repetition of 8-bar sections.

This is a standard that was probably more popular in the 1960s and 1970s than it is today.  It was actually written in the 1950s, but has a fresh, happy sound that is more typical of the following decades.
This song is deceptively simple.  The melody is interesting and memorable owing to some large interval jumps that remain within the diatonic framework (think "Somewhere Over the Rainbow").  And the song is a very conventional AABA form.

But don't get too comfortable in the A section because the B section (bridge) is in a completely different key center, presenting the same kind of challenge you get with tunes like "Have You Met Miss Jones?"
The A sections have very familiar changes in the key of F concert.  This uses the so-called "backdoor progression."  The usual ii-V progression in F would be Gm7-C7-F.  The backdoor progression is iV7-bVII7 or Bbm7-Eb7-F.  Many songs use this pattern, and it is well worth practicing this, just as you would practice a ii-V.  Here is a site that goes into more depth and lists a bunch of tunes where you will find this important little trick.  In addition to those jazz standards, there are many pop tunes that use the back door: e.g. Stevie Wonder "It Knocks Me Off my Feet" which goes straight to the back door in measure 3 and Billy Preston's "You Are So Beautiful" which is almost nothing BUT the backdoor progression.

So, practice the backdoor pattern to master the A section.  Then get ready to go with the flow in the bridge.  The first 4 measures are in the key of D major.  The next 4 measures are in C major, ending with a C7 to send us back to the key of F for the final A section.  Practice your scales in F, D and C to get warned up for this tune (and throw in some Eb practice to handle that backdoor business.)

Perdido is one of the most common tunes called at jam sessions.  It is a fairly simple tune of the AABA form.  In this case, the three "A" sections and 100% identical.  The "B" section follows the "Rhythm" changes (the bridge from "I've got Rhythm").  So it is a relatively simple tune to learn.

This song can be played in swing or straight Latin feel, with swing probably being more common.  This particular arrangement is in bossa style, so don't play swing 8ths.  However, you can impart a 'jazz feel" by emphasizing the offbeats while playing them in straight time.  The melody includes triplets, and you can integrate 8th note triplets and quarter note triplets into your improvisation.  Don't be surprised if it feels awkward to play this song without swinging the 8ths.  That is a good skill to practice.

There is a tag that is commonly played after the last chorus of this song.  That tag is included in this arrangement.

Here is the same song form in a swing style.  If you find one of these two styles distinctly more comfortable, that means you need to practice the other style more.

This Monk tune is typical of his genius/insanity. The melody couldn't be more simple.  There is a 4-bar melody that is played twice in C concert.  Then it is played up a 4th in F, and back down to C.  Then the whole 16 bar pattern is repeated -- except that this time, it is truncated to 14 bars followed by a simple 2-chord vamp.
That melody can be learned in a few minutes.  The hard part is the chord changes.  The melody points to simple, predictable chord changes, but not with Monk.  He aggressively re-harmonized these chords.  That's no problem when playing the head, but it creates a real challenge for improvising because you need to solo to the changes Monk wrote, not the changes anybody else would have written for this melody.  Take the time to really absorb these changes.

Here is a quintessential Coltrane tune.  The melody reminds one of "Giant Steps", but without all the giant steps.  That is to say, the melody is mostly based around the major 7ths and 9ths, which gives it that cool jazz sound, but the changes aren't as angular and unfamiliar as "Giant Steps".  This is a good tune as an entry point to the mind of Coltrane.

It is a simple 32-bar AABA song form, so that part goes very naturally.  The bridge has a very ordinary set of changes.  The A section is less ordinary, but not off-the-wall.  Spend a little time at the keyboard assimilating the chords in the A section.  That will be time well spent.

There is a long tradition of songs from the movies becoming jazz standards.  This is probably because once the songs become familiar to the public, jazz artists find the public more receptive to hearing those songs with a jazz treatment.
There is similar phenomenon where children's songs have become standards.  For example, "A Tisket, A Tasket", and "It's Not Easy Being Green".  In the present case, we have a song from a children's movie, "An American Tail".  "Somewhere Out There" has been performed by artists from Mickey Dolenz of "The Monkees" to Linda Ronstadt, Kenny Loggins, numerous jazz big bands and many small combos.
Here is an arrangement with a smooth jazz feel.  The song is AABA form with few complications.  Near the end of the B section, you find a single 2/4 measure.  Other than that, it is a rather normal flow with a small extension on the last A section.
In this arrangement, after the choruses, we have includes a little 4-bar vamp for some extra fun.

Blue Bossa is one of the more popular jam session tunes.  It is a very simple song form, so it is relatively easy to learn.  It is 32 bars, ABAB.  Usually when we say "ABAB" we mean that the A sections are similar or identical, and the B sections are "close enough."  But in this case, they are identical -- identical melody and identical chords.  So if you learn the first 16 bars, just play them twice and you know the whole song.

Harmonically, Blue Bossa is not terribly complicated.  Much of it is in C minor concert, so practice that C dorian scale.

Here a holiday favorite with a medium Cuban salsa feel.  Song form is AABB, 32 bars.  The chords are straightforward.  Have fun.

OK, it is that time of year again.  I know 2020 has been a beast, but let's celebrate the fact that the year is almost over.  Here's a seasonal favorite for your jammin' pleasure.