The old earbuds, yes, those always fall out of my ears.

The new-style ones that actually go into the ear canal do work fine for me (just have to find the right size plastic sleeves). But that's headphones, I don't think they would be comfortable if they were even a little bit heavier, and this thing has a battery builtin.

I used to have exactly the same problem until I found that the shape of headphones bundled with Xperia Z works for me - doesn't fell out and feels comfortable. I believe it's a matter of testing different models.

Same for me. The only comfortable earbuds that don't fall off when walking around are Sennheiser. The pair of CX300 I had were the best, though they had a short lifespan (< 1 year) due to the plastic cable.