I started out playing by ear as a kid.  In grade school music classes, I could do the silly exercises they gave us in music classes of spelling out words like "EGG" with written notes and etc.  But they didn't do enough with connecting it with sounds for it to be meaningful to me.  It was just written and may as well have been a math puzzle or word game. 

In 4th grade, we got a taste of playing an instrument, these things called "flutophones" which were sort of like a plastic recorder with a clarinet-like bell.  For the second half of that year we played those and got to go down to the music room and be taught by the school's instrumental music teacher.  I sort of was having more fun just playing with the instrument and working out by ear any tune I heard.  The teacher would always play any new piece through when he introduced it to us, and I'd listen carefully and memorize it, then practice it at home.  That worked until almost the end of the year when he caught me during a test by putting a simple written melody in front of me that I didn't know.  I got a stern talk about the evils of playing by ear and how I had good potential, but would never amount to anything musically unless I learned to read music.  That and my family not really being able to afford me taking up a band instrument turned me kind of sour on written music at the time. 

But I kept playing anything I could get ahold of, and I got a chord organ one year for xmas and an acoustic guitar another year and a little early monophonic synth and eventually got myself an electric guitar and amp, and taught myself to play them by ear.  I could follow chord charts and could sort of read music, but the notes were like using a decoder ring or something.  Credit where it is due, that very same music teacher was very supportive even though I was not taking any of his classes.  The topic of reading music came up from time to time, but I mostly dodged it.

I went on to play in bar bands and etc for some years, but eventually I did take "adult piano" in college and finally learned to sight-read.  It was good because I feel it really helped lock in the concepts of the theory classes I was taking at the time and I was finally no longer "music illiterate".  LOL  I consider standard notation as useful for a sort of universal language among musicians of the western hemisphere.  But I still play mostly by ear and mostly learn music by rote memorization, since I feel I put more of my emotion into a piece if I can play it off the top of my head by heart rather than reading it.  I do not consider standard musical notation as particularly intuitive for many instruments, though.  For instruments with enharmonic note possibilities like string instruments, I prefer tablature with some sort of time notations for reading and writing.  It just seems more sensible to me, but your mileage may vary.  I ran across some "fiddle tab" the other day, and that took no time at all to get used to and have some fun with.

I spent a good chunk of my life thinking of playing by ear as a "bad thing" musically, until I learned to sight read.  But now if people ask if I can read music I'd usually say "Yeah, but I try not to let it interfere with my playing.."

Midi is great, dashrem.  I also it for composing much of the time.  Or if there isn't any actual need for any sort of score, I'll often just record multitrack.  But I'm glad to be able to scribble out notes if I have an idea when I'm not near a computer or recording machine.  It is also helpful when working with another musician who picks things up quicker from the written. 

I'm only in my 3rd week with violin, but I would agree with you that there's something about it that makes playing by ear easier than many other instruments.  They have such an incredible range of sound for such a small and sensible little instrument.  Great fun to play.

I think that whether one is playing by ear or from sheet music doesn't matter too much in most cases.  The important thing is that we all play!

Here's my theory,,,, if you can hum it or sing it, you can play it without sheet music.

The note's are already there in your head, all you need to do is transfer them down to your left hand. If someone place's a brand new song in front of you and ask's you to sing the song, you probably can't. If someone play's the note's to the song then you can sing it because you know the melody, if you know the melody then you can play it. I'm not saying that reading note's is bad, reading note's is very good, but sometime's you need to throw your own stuff in there.

But i'm probably wrong about this too, I usually am.

In either case, you need control of the instrument. For me it's easier to find the note by sound rather than by note's.

Example: Musician's who are sightless. Ray Charles, Stevie Wonder and violinist Rin Ljima. Just couple who can't see music, it come's from their head.

Here is a perfect example.