My music teacher taught us to memorise and recognise intervals using the "compare-it-to-a-familiar-song" method too.
It works really well and Somewhere Over The Rainbow
was the exact song we used as well.
However, it's only effective if you're actually familiar with the tune - Also Sprach Zarathustra doesn't ring any bells with me.
So, as my teacher did, why not play the interval to the student and get them to name a tune they know which contains the same interval?
If it happens to be by some obscure X-Factor drop-out, so be it - they'll always remember it because they made the link.
If you're too proscriptive about the tunes they'll not be able to identify and remember them.
music.stackexchange.com/users/783/Widor
A great one to use for the rising major 6th is the "NBC" motif.
Fun fact, NBC was originally a subsidiary of General Electric, and instead of "National Broadcasting Company", "General Electric Company" was used, or G-E-C for short.
That initialism spells the notes that make up what is now known as the NBC motif!
music.stackexchange.com/users/133/NReilingh
M7:
Bali Hai, from "South Pacific" -- actually it's an octave jump up followed immediately by a half-step down, but you hear that M7 clearly.
West Side Story is all about tritones.
The signal whistle is G C F#.
Jet Song:
G G E C F#. Maria:
C F
# G. Cool:
C F# G
C First sung note of "Gee Officer Krupke" is an F# against C in the bass.
m2:
Jaws theme of course!
music.stackexchange.com/users/113/Mark Lutton
Since you're already using West Side Story: the canonical mnemonic for the tritone is Maria .
(In fact, I've never seen anybody use a different one.)
music.stackexchange.com/users/3083/Kilian Foth
m6 - 'Bei Mir Bistu Shein' (or 'Bei Mir Bist Du Schön') M6 - '
My Bonnie Lies Over the Ocean' (For most intervals I use(d) non-internationally known songs that I chose myself like Widor so nicely suggests.)
music.stackexchange.com/users/2245/Ulf Åkerstedt
Very nice question....
You brought back memories :)
My music teacher did the exact same thing.
I can't seem to recall all the songs she taught us though.
I remember she used Singing in the rain for Octave though! :)
Check out this link it has many interesting examples many of which my teacher used as well (like jaws, happy birthday, Superman Theme) http://www.musicalintervalstutor.info/listenpg.html Widor's answer presents an interesting approach I have to say.
music.stackexchange.com/users/3099/Panagiotis Palladinos
M3 (going down to tonic from major 3rd) =
doorbell...
ding dong.
Don't laugh - I still use it.
(Love the other examples!)
music.stackexchange.com/users/2851/Kristina Lopez
This site has an extensive list of songs corresponding to the intervals.
It's too much to reproduce here
but I will note that it's missing "O Canada" for the ascending minor third :P
music.stackexchange.com/users/None/
The stacked thirds from the bridge of Twist and Shout by the Beatles.
It gives you the whole layout of the scale in one meme.
music.stackexchange.com/users/1344/luser droog
As the tutor for my school's music department, I spend a lot of time helping students drill intervals.  However, I only have a handful of songs to recommend recognition.  P8 — Somewhere Over the Rainbow P5 — Also Sprach Zarathustra P4 — Here Comes the Bride m7 — Somewhere (West Side Story)  And there's the extent of my help.  Everything else I work as either arpeggios or scales.  What are good pieces to help my students?  Particularly Tritone and the Major and Minor 6ths.
Musical Aids to Memorize Intervals
music.stackexchange.com
<theory><intervals><ear-training>
music.stackexchange.com/questions/7805
music.stackexchange.com/users/3169/user3169
A great musical aid to use for the rising major 6th is the "NBC" motif. For West Side Story, the canonical mnemonic for the tritone is  Maria . Some good tunes for helping students to memorise intervals include the NBC motif for a major 6th and Maria from West Side Story for a tritone.
Some good tunes for helping students to memorise intervals include the NBC motif for a major 6th and Maria from West Side Story for a tritone.