I have a TRX 125 Honda Fourtrax 1986 model and I am having trouble getting it to run. There is spark and fuel but it seems to be a problem with compression. What strikes me as weird is that as long as the ATV is sitting flat it has no compression but if I stand it up it will have compression. I found this out by trying alot of different things. I don''t understand this it seems to me that if it has compression standing on end then it should have compression sitting level. I consider my self a pretty good mechanic and this is drying me crazy. Any ideas?  

could be a bad cylinder gasket.

what you may be experiencing is that when you stand it on end oil reaches the cylinder gasket and causes it to seal enough to get a little compression.

whereas when you put it back down the oil spreads out evenly in the crankcase making it shallower.

perplexing though.  

I am assumming you did a compression test.
I just purchased an 1986 4trax 125 this weekend for $100.00.  It was not running for over 3-4 years.

Basic Steps I took to get my running within a day.
Diagnose....for sure you are getting spark.  Make sure the you have good solid spark on the plug.

Determine if you are getting good fuel flow....very easy for Carb to pick up sediment and not start at all.
I pulled apart my Carb and cleaned and blew out all jets with an air compressor.  I then put a inline fuel filter on the main line between the tank and the main feed to the carb.  

I pulled the plug and sprayed WD40 in the piston head....yes. WD40.  In about 2-3 three cranks it fired up and stayed running.  Idle is a little off but other than ...runs like a champ.

I honestly feel you have a fuel issue..if you pull on the start...do you have any compression at all with the plug in tight?  I had people tell me I had blown rings and stuff...but I tried the basics and it worked.
Hopes this helps...