While The Beatles are best known for their many great guitar based songs (such as "Get Back," "Revolution," & "Day Tripper" to name just a few) they also had a number of excellent songs where the piano was the main instrument in the mix.

"Hey Jude" - This was one of the Beatles most successful singles both as far as sales (it went to #1 in the US & UK along with nine other countries) and as far as critical reception. It was nominated (although it did not win) for three Grammy Awards (Record of the Year, Song of the Year, and Best Pop Performance by Duo or Group with Vocal.) It won a 1968 NME poll for best single of the year. And in 2004 it was ranked as the 8th greatest song of all time by Rolling Stone magazine (the highest ranking Beatles song.)

For a long time it was the longest #1 single in US & UK history (it's just over seven minutes long.)

Paul McCartney wrote the song, played the piano, and sang lead on the song (as he did on all three of the piano based songs in this article.)

"Let It Be" - The title track for The Beatles final album was another hugely successful Paul McCartney piano ballad. It was also included in the 2004 list of the 500 greatest songs of all time by Rolling Stone magazine (#20.) Over the last six months it has been the most played Beatles track (barely beating out "Come Together") on the music site Last.FM ("Hey Jude" is #6 on the list.)

While this song is definitely "piano based," the guitar solo by George Harrison is one of the more beautiful guitar solos I've ever heard, and does deserve a mention when talking about this timeless song. 

"Lady Madonna" - While not as famous as the previously mentioned songs, it did go to #1 in the UK (where "Let It Be" actually only reached #2.) Although it did reach only #4 in the US which is actually a low ranking for a Beatles single!

Unlike "Hey Jude" & "Let It Be," "Lady Madonna" is a fast paced rock song. Along with the piano, defining features of the song are the heavy bass guitar, the saxaphone, and the unusual sounding backing vocals. The song is barely over two minutes long which was normal for The Beatles, but would be quite strange for a single today.

It's been the 28th most played song on Last.FM over the last six months (right above the early Beatles hit "She Loves You.") 

In the 1990s the band Sublime had a hit with the song "What I Got" whose melody is almost identical to "Lady Madonna."