I want to hear you stories, and share some of my own.  Tell me about the one that got away, didn't take a step no matter what you did, or wouldn't slow down long enough to get anything done. 

For our difficult to catch we had a myriad of Galicenos that had been raised with minimal human contact after the first year. They were all halter broke, some lead broke, but still very wild.  Of these we had a pair of full brothers, 8yo Flash and 6yo Peanut Butter.  Both sons of El Cacahuatito (sp. Peanut) and Miss Lightening.  Both are buckskin(Dun factor) gelding and are thick as thieves with one another.  If one runs, so does the other.  We tried everything.  We ran them back up the hill into a catch pen.  That work for all of about 3 captures.  We tried treats, but neither would eat out of our hands.  Then we tried grain.  Sweet feed.  That got to Flash.  He would eat and if you moved ever so slowly, you could slip a lead rope around his neck and catch him.  Peanut Butter, however was a runner to the end.  We once caught him on the banks of the creek where it was a sheer 20 ft drop, cornered and with us on either side.  We had stretched the lead line between us and worked around him until we could almost reach one another again.  One tossed the lead to the other and he was caught.  Our favorite method is the hug.  Walk up and throw our arms around them, lead in one hand and drag it around until the hose is secured, but it has become too obvious what we are doing.  We have had to be creative.  Another time, I had the welsh mare, Honey. She was badly buddy sour and lazy as all get out from languishing in a paddock on a cutting horse ranch, unused.  She buddied up to Sierra, my Galiceno filly and daughter to the lead mare.  As long as Sierra was between her and Rosalita, she was safe.  She would use Sierra to try to get away from me by making her run with her and staying on the other side.  I had already taught Sierra that my approach was a good thing.  I simply began catching Sierra first and just waiting.  Eventually Honey would come up to investigate and allow herself to be caught.  It was a long summer fixing her personality quirks. She was super spooky and poorly behaved under saddle.  Time and perseverance worked that out. I never gave up at her refusals and pawing.  I kept riding her daily and she eventually got to where she was dependable.