I'm a non-EU citizen with a 90-day work agreement for Germany as a sort of student program. After these 90 days, I want to stay for no more than a week to go on a vacation with my girlfriend. But the vacation is also in the EU, so do I have 90 days as a tourist in the EU because of my work agreement or will overstaying for a week cause no harm?
I would assume that you have to leave the EU and apply for a visitor visa again. From a report on Euro-Dollar-Currency.com:
Overstaying Schengen visa can be very expensive. One traveler is known to have been fined 700 EUR by the Greece embassy after 20 days of overstaying Schengen visa. He had two options, either to pay a 700 EUR fine to the embassy or not to pay the 700 EUR fine but then not be allowed to get back to Greece and the whole Schengen zone for 5 years.
I really wouldn't risk it, more so, if you plan on going back to Germany or other Schengen states in the near future.
EDIT: Found this answer on a similar question:
I had the same situation as you. I decided to leave the Schengen area when my work visa expired (hopped over to London for the weekend) and came back through Paris. I had no trouble at border control with getting an entry stamp, and the border agent hardly looked at my expired visa.
seems like you will be fine if you just leave the Schengen area and go right back in. On the other hand, other answers on the question mentioned seem to suggest, that you get the 90 day tourist visa automatically after your work agreement expires, but I find that hard to believe.
The French Consulate in Sydney specifically says you should leave Schengen and reenter it:
If you want to stay in the Schengen space (for up to 90 days) at the expiry of your working holiday visa, you will have to leave France and the Schengen space and re-enter the Schengen area the following day as a tourist for 90 days within a 6 months period. You may leave the Schengen area (passport stamped at the border) by going to the UK for example.