Mozart
Concerto for two pianos in Eb major (All of it, though the slow movement is especially wonderful for very new babies to nap through.)

Kreisler
‘Rondino’ for violin and piano

Debussy
‘Clair de lune’ for piano

Delibes
‘Flower Duet’ from Lakmé

Puccini
‘O mio babbino caro’ from Gianni Schicchi

Mozart
Andantino from Concerto for flute & harp in C, KV 299
Piano Concerto no. 13 in C, last movement
Piano Concerto no. 17 in G, first movement
Piano Concerto no. 20 in D (the slow movement is perfect for babies, the first a little dark but oh so beautiful!)
Piano Concerto no.21 in C (this is my favourite)

Bach
Allegro from Brandenberg Concerto no.3, BWV 1048
‘Badinerie’ from Suite no.2, BWV 1067

Chopin
Prelude no.15 in Db major for piano
Nocturne no.9 in B, Op.32 no.1
 
Waltz Op.18, ‘Grande Valse Brilliante’ in Eb
 
Tchaikovsky
Waltz from Sleeping Beauty

Beethoven
ANY of the Piano Concertos they are all AWESOME!

Morricone
Gabriel’s Oboe (had to include this for my son Gabriel – it was played at one of our very first concerts in 2010; a little ‘crossover’ maybe, but beautiful!)

Williams
‘Hedwig’s Theme’ from Harry Potter (Before you can say “Harry Potter is classical?!” – the mighty John Williams is thoroughly respected in the classical music world.)

Richard Strauss
‘Beim schlafengehen’ Going to sleep from Four Last Songs. What the hell, listen to all four. (WARNING: Get the wrong singer’s recording and you might hate it! – Try Lucia Popp singing with the London Philharmonic in 1982, it’s not too warbly, just divine!)

Mozart
‘The Marriage of Figaro’ – the DVD of the Glyndebourne 1994 Production

Albéniz
‘Asturias’ for solo guitar (from the album ‘MILOŠ – The Guitar’)

Tarrega
‘Lágrima’ for solo guitar (see above)