I've read/heard a few famous musicians (Donovan was one, but can't remember the others offhand) who said that they realised the first time they heard Love Me Do on the radio in late 1962 that this band was something different.
I bet it was a very influential song on the Mersey Beat scene - it got into the top 20 in the national charts, which was the first national recognition for any of the Mersey Beat bands. And it was the Mersey Beat bands - led by The Beatles, obviously - that stormed the UK charts in 1963 and then helped to push the British Invasion in the US the following year.
So my vote would go to Love Me Do.
It's certainly not their best song, or one of my personal favourites, and it sounds quite twee when compared to what came later, but I think it was ground-breaking in its own way.
Other ones that I would say have been influential.....
Please Please Me - their first big hit in the UK, and a sound that inspired a whole host of bands to copy the Beatles style
I Want To Hold Your Hand - their first big hit in the US, so will have been a big influence and inspiration for young people there
Hard Days Night - Roger McGuinn says that jangly guitar sound made him want to stop being a folk singer and take up the electric guitar
Yesterday - the first time they tried something really different on record, and it is now the song with the most recorded cover versions ever, so it must have inspired and influenced somebody!
Rubber Soul - that whole album inspired Brian Wilson to take The Beach Boys to new places when recording Pet Sounds
Norwegian Wood - the use of sitar was very influential and was widely copied, most famously by The Stones on Paint It Black
Hey Jude - there had been several hit singles before this that had broken the 3-minute barrier, but The Beatles really showed that music was now about more than just the 3-minute pop song
Revolution 9 - influential in the fact that it showed other bands that it was OK to experiment in the studio and take risks