I learned this too late in life.  Whether you’re just getting started with music or have been playing for a long time, get yourself a pan flute (or zamponá).  Something about having to move to a different part of the instrument for each note by feel of the distance rather than by sight (as on the piano) has really helped my sense of the relationship between notes.  I noticed a very quick improvement playing guitar and (separately) picking out melodies.

If you’re interested, I recommend Brad White’s pan flutes.  (Go ahead and buy the corresponding case when you order it.  You’re going to want it.)  I haven’t found a good supplier of zamponás; the one I bought at a local music store was inexpensive, but it’s pretty much a toy, and I had to shove cork in some pipes to make it tolerably in tune.