When I was faced with the same issue I used aluminum foil and waxed paper to get a meter into the battery circuit of my Pentax digital camera. If you want something more permanent try a piece of one of those almost impossible to open plastic blister packs with copper strips super-glued on. Solder the wires to the copper strips before you glue them to the plastic or you'll have a sloppy mess. That should be thin enough for what you want.
Everyone sells 0.8mm which is the next standard size down. Most PCB suppliers will go down to 0.5mm as standard, and thinner if you ask them. The thinner stuff (down to 0.1mm or below) is actually pre-preg or core used in multi layer PCB's. It is actually surprisingly flexible and you can actually use it as "flex PCB" in designs that call for a curved board that doesn't move after installed.
Awwwww! Sorry about the awful typos! Blush. The English version of what I mean to say is ...
I want to create a probe to put in between two AA or two AAA cells to determine the current flowing. The probe could be made up of a piece of double-sided circuit board with a wire coming from the contact area on each side. All I see in the catalogues is 1.6mm PCB. Where can I get a bit of thinner board?
On 22-Mar-2009, IGNORE what john wrote WITH THESE TYPOS...
WORK ON THE WAY OUT OF USENET IT IS NOT YOUR PERSONAL LITTLE BUSINESS DEVICE IN CASE YOU HAVEN'T NOTICED ARCHIMEDES' YOU HAVE BEEN DEAD FOR YEARS YOUR LEVER HISTORY TRY A PCB SHAKE WITH YOUR LUNCH AND REJOIN REALITY
You can take bare stock of FR4 or G10 variety, which can be had down to like 0.015" inch (perhaps thinner).
It is very stiff, and you can place conductors across it and put Kapton tap over the conductor, leaving a hole in the "contact area". Do the same on the other side, and take your readings from the leads you attach.
You'll get better results as the strip you use will be heavier gauge than any PCB cladding could ever be.
I would fan out a simple piece of Teflon (PTFE) insulated, Silver Plated Copper (SPC) stranded wire. You fan out a strip length of a few mm, and place the Kapton tape with the hole in it over the fanned out area. Same on opposite side. Kapton over the "nose" of it lets you slip it right in.