They're not cut with a saw, they are shaved with planes.

Laszlo

   can you elaborate that?

https://www.youtube.com/watch?v=y0BW-dxYiBY

   A table saw, with a blade stiffener, a true fence, a tight throat, and cutting a strip so that the piece you want is the off-cut that peels away, can easily cut 1/32" strips. 

I've used a bandsaw to cut very thin strips(1/8").  Depending on the blade, you get a rough surface in the kerf.  You can then sand them thinner with a random orbit sander and then as thin as you want by hand. You don't have to stop until you start getting holes through the strips.  It is a finicky and time consuming operation, though.

Hooper Williams - Brevard, NC  

YouThere are even thin rip guides for table and band saws   

http://www.rockler.com/thin-rip-tablesaw-jig

http://www.woodcraft.com/product/152627/magswitch-ultimate-thin-stock-holddownrip-guide-tool-attachment.aspx

The uncut stock buts the fende and the rip guide is on the opposite side of the saw blade. The roller keep the stock tight against the fence and the cust strip is on the outside of the saw blade and not pinched against the blade.

You should use a zero clearance insert so none of the thin strip falls between the saw blade and insert plate.

   Thank you all for your reply.  I notice the way that was explained, thestrips are ripped off the stock laterally. What if the stock you need the strip verticully?  For instance the typical cedr strips that are from CLC for the kits.  I want to cut an accent strip off the bottom of the aforementioned strip.Or I want to cut the cove or bead off. A nother example.  I want to keep the bead on but have the strip itself shorter highth wise.  they come 3/8 inch but I want a strip that is a 1/4 in with a beadon the top or a cove whichever is neccessary.

   Time to sharpen your plane. A good plane will do all that, just keep the blade sharp. One has to get creative to clamp the pieces while planing them. Sometimes I clamp one end right to my bench and plane the other end, and then switch. A sharp plane cuts with more precision than any power tool.

One can lay down the strip and then orientate the stock to cut off the unwanted material. If one wants to stop short of the end of the cut, then a table saw might not be the best solution. For such a cut one could use a track saw (a metal track is laid over the material one wants to cut and then one aligns the saw on the trak and pushes the saw along the track) and does a stop cut at or near where one want to stop the cut. A Festool TS-55 REQ can cut a strip as thin as 1/32" and with enough properly aligned tracks cut for will over 20 feet.  I'll warn you, you will be paying as much or more for the Festool TS-55 than you paid for your table saw.