All 10 of these songs (and many more) can be heard in awesome remastered sound in these "greatest hits" collections: 1962-66 (Red Album) and 1967-70 (Blue Album) CDs. These two sets of CDs are a great introduction to the band. They're actually how I first got into The Beatles many years ago (I'm now a huge fan who has every thing they've ever released.)
All of The Beatles albums are included in The Beatles in Stereo Box Set which is strongly recommended for all serious Beatles fans. This is the way to hear The Beatles! (and the really serious Beatles fans need to pick up the Beatles in Mono Box Set too to hear their albums how they were originally meant to be heard.)
Included below each song is a Daily Motion video featuring that song. Daily Motion is used because their videos usually have better sound quality than YouTube videos. Although you'll definitely get better sound quality by purchasing The Beatles albums on CD or on vinyl.
The Beatles Top Ten Most Popular Songs Of All Time
#1 "Let It Be" from 1970's Let It Be.
#4 "Eleanor Rigby" from 1966's Revolver.
#5 "Hey Jude" from Past Masters Vol 2. (non-album single.)
#6 "Lucy in the Sky with Diamonds" from 1967's Sgt. Pepper.
#7 "All You Need Is Love" from 1967's Magical Mystery Tour.
#8 "Help!" from 1965's Help!
#9 "Something" from 1969's Abbey Road.
#10 "Here Comes The Sun" from 1969's Abbey Road.
Four of the top 10 were written and sung by Paul McCartney (1, 3, 4, & 5.) Four were written and sung by John Lennon (2, 6, 7, & 8.) And two were written and sung by George Harrison (9 & 10.)