I've seen this problem listed a lot on various message boards, so I thought I'd clarify the problem for those of you faced with it. Many have said they replaced the head gasket or valve seals, but the problem still exists. The problem is not with a gasket or seal, rather the oil rings.
The Mazda B2200 and 626 engine blocks have a high nickel content in the alloy making them a very hard metal. The smoking problem can be caused by two things. First, the oil rings can simply lose the friction battle with the hard cylinder walls, making their function ineffective. Second, and more commonly, the oil rings get stuck in the groove by oil carbon deposits built up on the ring, also rendering them ineffective. The problem generally occurs after 100K miles, and causes the engine to fail emissions even if the smoke clears up after the engine warms up.
There are two possible solutions; re-ringing the engine or a complete rebuild. Because the engine block alloy is so hard, the cylinders tend to wear very little and in some cases the original honing marks are visible. If you choose this route, you should thoroughly clean the pistons and the ring grooves with a good solvent that breaks down carbon, like Chemtool. Easy-Off oven cleaner works too, although not as well. Clean all of the internal parts and surfaces of the block, de-glaze the cylinder walls with a quick honing, replace the rings and reassemble the engine. Some smoking may occur during the initial break-in but this is normal. Remember, also, if your engine was passing a great deal of oil that there is likely an oily residue in the exhaust system which will smoke until it eventually burns out of the pipe.
Of course, if you have the engine apart, you should have it checked for wear. If the cylinder walls are excessively worn, re-ringing the engine will not help you, at least, not for long.
I have a B2200 that a friend gave to me (yes, gave... as in free). When I disassembled the engine, I found the oil rings completely recessed in their grooves on 3 of 4 pistons and I had to use a machinist's scribe to get them out. The engine had some cylinder wear, mostly skirt wear causing the cylinder to be out-of-round, so I'm doing a complete rebuild. Shop around for parts, as their prices vary widely.
After you re-ring/rebuild, prevent this problem from re-occurring by keeping up with oil changes. I would also recommend considering the use of a synthetic oil, although good oil maintenance as well as engine maintenance in the form of tune-ups should suffice in preventing a re-emergence of this problem.
If this sounds imposing, it's really not. I'm a technical writer by trade and my car/engine work is a shade-tree hobby. If you've rebuilt engines before, this task should pose no problem to you. If you have any questions or need more information, email me at email@example.com.