I don't know how you define this. I only started guitar about 2.5 years ago. I made very little progress till this year when I started with a teacher and actually got some quality guitars. Particularly at first I feel like you're not really "learning the song", you're learning a bit of a song that you can handle and that lets you learn what you need to learn. I first worked by myself with the Hal Leonard Guitar method.. not a terribly well thought out book in retrospect. First melody in there is a single note version of Ode to Joy. The book is really kind of odd in the early stages, it's way too much like they took a piano course and deleted the left hand and just made it for guitar. Weird approaches to chords and very little info on the physical aspects. The first tune in there that's pretty good to play is probably Greensleeves. It's basically all public domain music. First song I worked on with my teacher was the vocal melody to "Every Breath you Take" by the Police, plus a beginner chord arrangement to play as an accompaniment. That was before I had an electric guitar. I took lessons for about 3 months before getting my Telecaster, first song I worked with the Tele was "Walk Don't Run" by the ventures. I played most of it, but couldn't play the whole thing cleanly at a good tempo particularly the chords. I have been revisiting that lately, if I can memorize the whole thing I can play that pretty nicely now. For some reason the structure of it has made it hard for me to memorize, but if I put a week of daily practice into it now I'd have it and then I probably wouldn't forget it. First song I could actually play the entire song within reason was "Living Loving Maid" by Led Zeppelin, to date it's the only song I learned the guitar solo on. Of course that song is overdubbed in the studio with a slide guitar part, I didn't learn that, I've never even tried a slide. The first songs I can play basically the whole song, at tempo along with the recording and sound presentable are Harvest Moon and Heart of Gold by Neil Young, I can almost sing Heart of Gold while I play too. Pretty big milestone. Those two are within the past 6-8 weeks so very recently. I was 38 when I started.. for some reason playing has increased my ability to memorize stuff a lot. Neat mental benefit. That only came when I started working on playing without the sheet music. I worked on piano for quite a while and my memorization never came along the same way.