A horse that has been trained through gentle and positive techniques will normally allow a rider to mount him without incident. However your horse may become shy about letting you get on his back and there are usually two main reasons why:

Improper Mounting
All horses need consistency in training. Horses only need one bad incident to undo a lot of good training. If an inexperienced rider mounts a horse and makes it a painful or unpleasant experience, the horse won't forget that and may become skittish about any rider mounting him.

Pain
If an otherwise amiable horse suddenly becomes shy about being mounted, he may be feeling pain. Check him for saddle sores; a too tight cinch or other areas that may be making him feel discomfort. If he still seems uncomfortable, have him examined by his vet.

Solutions
Retrain your horse. Be consistent and show your horse that being mounted will not harm him. This will take some time to build his trust in you back up but it is the easiest technique to allow your horse to be ridden again. Give him the command to stand and slowly mount him. If he becomes upset, skittish or attempts to bolt, talk to him softly and soothingly and assure him he is okay and see if he will calm down. If he will, attempt to mount him, if he won't walk him around his pen and talk to him so he can calm down.

Use of a saddling block might help things too. This allows the rider to step up to the horse and if you rub your horse all the while so he knows where you are, you can stand on the block then gently transfer your weight to your horse and most horses generally allow this method when straight mounting fails.