Not a fan. Listened to them a lot as a kid, in no small part because my father loved them and if my old man liked it, it had to be awesome. Nowadays, I find most of their songs annoying and even the good ones aren't anything special. I also think that their influence on 'modern music' is seriously exaggerated.
Something that hasn't been mentioned is that the Beatles really helped to pioneer the idea of the music album as an art form. Before the Beatles, albums were basically meaningless cash-grabs by the record company: An Elvis record, for example, was usually just Elvis singing a bunch of random songs everyone was already familiar with. The Beatles not only wrote their own songs but took a great deal of control over their recording careers in general, which was absolutely unprecedented for the time. Albums became planned "music programs" by the artist; thought was given to the quality and order of the songs on the record, and even artwork was something the band had control of. This is becoming a lot tougher to appreciate now that "albums" are once again fading away as the main way of listening to music, but anyone in the last 40 years that grew up with a "favorite album" has the Beatles at least partly to thank for creating the concept.
To the original topic, there are probably a lot of bands who have one or two songs I like more than the Beatles', but what makes the Beatles significant for me is the consistent quality of the songs they put out. Most albums have maybe one or two A songs, a couple C songs, and several F songs. The Beatles, with few notable exceptions ("Honey Pie", I'm looking in your direction), never made a song that was less than a B-. Over 250 songs, that amounts to an outstanding level of quality. So while there are probably bands that have better "hit singles" than the Beatles, for me there is no band that has better "track 11 on an album" songs. That's what makes the difference.
But if that is true, I am still very grateful that they were around, doing the things they did. I
love the idea of a music album as a single, coherent piece of art and wouldn't ever buy songs online separate from the album they're from.