Where the teeth come out of the wood, you can get splinters. The faster the cut, the larger the teeth, the more perpendicular to the surface and the duller the teeth, the more splinters you will get.
For a hand saw, the splinters are on the bottom of the wood. For a portable circular saw, the splinters are on the top of the wood. For a table saw the splinters are on the bottom of the wood. For a Radial Arm Saw, the splinters are on the bottom of the wood. For a sliding mitre box, the splinters are on the top of the wood.
When using round saw blades, the angle at which the blade comes out of the wood is important. If you have a circular saw with the shoe set to maximum depth, you will get more splintering than if you set it so that it will just barely cut through the wood, because the angle that the teeth come out of the wood is lower to the wood when you are working on the outside of the curve of the blade. Of course a very sharp blade and a slow cut will reduce splinters tremendously.
Applying masking tape to the cut and cutting right through the tape will help as well because then the neighbouring fibres are supporting the one being attacked by the cutting tip. Be careful to not use a tape that will leave a glue residue that can effect your finish.
The cabinet making tip is to score the cut line with a sharp knife, essentially cutting off all the splinters before making them. Then saw right up next to this cut, without hitting the cut itself or crossing over to the other side. You will still create splinters, but they will break at the cut line and there is not pressure on the fibres the other side of this line.
In the photo I was way off of the cut line just to show how the top fibres lift and break at the line. For a precession cut, just keep your saw teeth on or outside of that score mark and you will have a perfect splinter free cut.