Of course it's possible. If you want to catch a Mewtwo without a Master Ball bring strong Pokemon, buy plenty of medicine to heal your pokemon (Mewtwo knows Recover, so watch out for that), buy as many Ultra Balls as you can afford (VERY important), and save before you make an attempt to battle it (of course). Whittle down its HP, try to inflict it with status (as was said before, freezing is the most effective method, but paralyzing it or putting it to sleep are easier), then just throw Ultra Balls at it like a madman. In other words, just do the same thing that you would do with any of the legendary birds.
The truth is, Mewtwo is no more difficult to catch than Articuno, Zapdos, or Moltres aside from the fact that they are all at lower levels and can't recover in battle. They all have the same catch rate (which is 3, the lowest possible for any Pokemon). If it's possible to catch all three of the birds without a Master Ball, it's possible to catch Mewtwo.
Well said, I completely agree. On HG I caught Mewtwo with a Quick Ball ( in my vid!) and in LG it took awhile longer but I caught Mewtwo with an Ultra Ball. That's all I can remember!