English riders are taught to always mount from the left hand side of the horse (near side).  This "tradition" stems from when people used to ride horses and carry swords for battle.  If they were right handed, which most people are, they would have their sword sheath on their left hip.  So most people would mount from the left, otherwise they would trip over their sword or accidently smack their horse with it.

This probably explains where the tradition of lying horses mains on the right hand side comes from also, to keep it out of the way when mounting.   I was always taught to lead from the left too, which makes sense for the sword carrying people as thats is the side they mount from.

However, I do not, and never have ridden with a sword, so there is no reason for me to mount from the left all the time.  In fact, if I always mount from the left, I will become one sided and will only be able to mount from one side.  My horse will also become one sided and so will my saddle, with the left stirrup leather being constanly stretched, making it longer than the right, which will make me unbalanced when I ride, which will unbalance my horse also. 
Always leading from the left is just as bad, your horse will not feel happy with you being on his right side, everytime you want to go on his off side, he will somehow wiggle his way back on your other side, or generally mess about until you are on his "good" side again. 
This becomes evident when lunging.  Most horses who are always led from the left, will lunge fine on the left rein, but will be totally against going the other way.  They will spin around and put themselves back onto the left rein.  This is partly because they are used to seeing you on their left, and partly because they won't be as flexable on the right rein as they are used to bending their body towards you on the left.  They will also be better on the left rein when ridden, and will feel uncomfortable on the right.

You should mount equally on both sides if you can, even though mounting from the right will feel very strange at first, both to you and to your horse.  This will even up your stirrup leathers, as well as your legs and you horses back muscles.  You should lead from the left, and from the right so your horse will get used to you being on both sides. This will help him become equally flexable on both reins, and will stop him feeling awkward when on the right rein.  Your horse should be comfortable being led from the sides, in front and eventually from behind.