As per the title. What are the dimensions of a business card that fits in a wallet? (i believe it is a global standard?)
Bonus marks if you can give the history behind how it arrived at that dimension.
It is not as standard as one would hope of. The common aspect ratios range from 1.423 to 1.8.
For the most ID cards and credit cards ID-1 from ISO/IEC 7810 (wikipedia) standard tells the dimensions, which are 85.60 × 53.98 mm (3.370 × 2.125 in) and aspect ratio is 1.586. This is also the standard business card size in many situations as it is highly pocketable.
Other size, which could be considered somewhat international, is the ISO 216-sized (wikipedia) A8 = 74 x 52 mm (2.913 × 2.047 in) and aspect ratio is 1.423. Though, personally, I haven't seen much of these.
There are a few cultural variations. For example here in Finland 90 x 50 mm (3.543 × 1.968 in) is common, but ID-1 size is also quite common and 90 x 55 mm isn't totally oddball. Wikipedia article on business card dimensions has a good table for reference:
# mm inches aspect ratio (1) 74 x 52 2.913 × 2.047 1.423 (2) 85 x 55 3.346 × 2.165 1.545 (3) 85.6 x 53.98 3.370 × 2.125 1.586 (4) 90 x 55 3.54 × 2.165 1.636 (5) 91 x 55 3.582 × 2.165 1.655 (6) 90 x 54 3.543 × 2.125 1.667 (7) 88.9 x 50.8 3.5 x 2 1.75 (8) 85 x 48 3.582 × 2.165 1.771 (9) 90 x 50 3.543 × 1.968 1.8
For international, common use, I'd suggest the ID-1 size as the size is familiar to many, it is highly pocketable and isn't as culture-oriented. And it is more widely used than the A8, I think.
Actually, even for one-country use I'd first suggest the ID-1 to my clients (tell them it is the credit card size), since the size is easier to get a grip on (for them). Client could get a credit card from hishers wallet and imagine the business card layout on it and feel the size in hands.
But some may have personal biases towards the (non-standard) national size, so I would offer it as an alternative. Some may have previous business cards (or someone else's) and would want the same dimensions. For the designer, the ID-1 size is helpful in this occasion too, because when you first ask what sized business card they want — and the client answers "Business card size, duh!!!" — you could ask: "Is it the same size or bigger/smaller than your credit card?" And the answer, with the help of the business card dimensions table, probably solves the actual size. (Been there, done that.)
Also it should be noted that the business card culture in East-Asia has more weight than in a regular Western country (see e.g. an article on Ezine). In China, business card etiquette has seemingly complex traditions and in Japan the business cards are highly respected. If your client is about to do business in either, I'd suggest to design the cards according to China's/Japan's most common size, or do a separate run for Asia usage. (Note that China's and Japan's common business card sizes differ from each other).
It's also recommended to consider unique variations, as using slightly different sizes in business cards can make yours stand out from others. If one happened to pick up multiple cards at a trade show, all of them will stack together nicely. The random one that is a different size from the rest will stand out, and probably get noticed easier.
Koiyu said it right there is no one fix size. You can also stick with the same size as Credit card, that will definitely fit in someone's wallet :)
On a side note check this out http://us.moo.com/products/minicards.html, they are unusual and that is what makes them unique. You may not want to have same business card with same size and look like everybody else..:)