I've read that I can stay for 30 days in Singapore without a visa or without extending my stay. But can I stay 30 days in total or can I stay up to 30 days each visit?
I'm from Germany and only have a passport.
As usual, the answer is 'it depends'. I traveled in and out of Singapore several times and I always got a new 15 days (you only get 30 or even 90 days if you fly in).
But if you go over to Johore Bahru on the other side of the bridge in Malaysia for the morning or the night and then come back, you wont get a fresh 15 days, because that would be considered a visa-run.
I think if you fly in and have been away for a week or more you should be fine.
Only certain countries require a visa to enter Singapore and Germany isn't one of those countries. Here's a list of those countries: http://www.ica.gov.sg/services_centre_overview.aspx?pageid=252
If all goes well, you should be granted a 30 days social visit pass. The immigration office has the power to give you anything less then 30 days or even reject your entry.
Once you're in Singapore, if you'd like to extend your visa, you can go online to do so. You will get another 30 days if successful. You can also cross into Malaysia by bus/car and when you return you will get an extension of 30 days. Of course, again, it depends on the immigration officer.
I did a trip last summer during which I entered and left Singapore twice during a trip and when I came back the second time I got a new 90 days stay. The same thing happened to me during another trip.
So you should get 30 days (or 90 days) for every visit. The number of days that you actually get will be stamped into your passport. (It's quite small in the fine print that runs around the stamp)
You can find more information on the website of the immigration agency.