My experience was very subtle and I have never actually come face-to-face with Herobrine.
Around Minecraft 1.0.0, I made a small house near a cave and started mining iron. It was nighttime. I went into my house and I heard the sounds of someone walking on the wooden roof. I looked and there was no mob on the roof.
I was confused but accepted it. Then a few days later the sound came from my floor. A few days passed, all the same.
I got tired of this and went mining again. There was a vein of iron that I had missed. I left to go get my stone pickaxe after I realized I forgot it. I went to get it and came back and saw that the iron ore was completely gone.
My friend JAKIEJAKIE's experience
The next week in real life my friend called me and he was shaken up. He was playing the snapshot for 1.2.5 and was in a ravine when he saw what he described as "A floating head of the default skin with white eyes" in the void fog. He ran away and never saw it again.
Still I don't know how to make sense of these occurrences.