I don't think there is a universal system, no. Some of the numbers I have seen have been 10,000 shares, 100,000 shares, 1,000,000 shares. (When creating options a large number of shares with small denominations makes it easier to hit odd ownership percentages -- say 1,133% for example -- without having to issue new shares.)
That said, there could be traditions or specific legal considerations that apply in your home country. The best source of advice would be a lawyer who regularly incorporates startups.
It's all essentially virtual, so you can 1,000,000 or 638. Or any other number.
Generally speaking, the more partners and/or money raises you expect to do, the number of allocated shares will be higher.
You also don't have to get it exact the first time. You can always issue more shares let if needed.
Keep in mind that the annual "franchise taxes" that your company may have to pay could depend on the number of shares authorized- more shares = higher taxes.
Your state may differ, but for Delaware corporations, there are 2 ways of calculating those franchise taxes; go to the Delaware Secretary of State website here to see more:
Yes, therte is a system. THe number must be dividable by the shareholders indented. If you want 3 equal shareholders, 2 shares wont do it, neither will four. You will need a multiple of 3.
That is about it. The rest is up to you.
In addition to what Jesper said, I've also seen cases where the number of shares was 100 or 1,000.
In the case of 100, that was when the company was owned by one or two people, with little likelihood of adding additional shareholders later. As such, there was no need to complicate tracking with a large number of shares.
With 1,000 shares, that was with a company that was considering adding additional shareholders, but not raising capital (which may have required share dilution with the creation of new shares).
as many or as few as you like, depends on how you want to divide up the company. One way of doing this is based on current investment in the company. if you have put in 10,000 and a partner has put in 5,000 then you could do 3 shares, with a 2:1 split.
Also bare in mind that share value can be diluted by issuing more shares.