Some beers (for example, Guinness) are marked as 'not suitable for vegans'. What is in the beer such that this is the case?
There are two main ingredients in beer that might cause them to be unsuitable for vegans. The first one might be fairly obvious. Honey is sometimes used as a sweetener, especially in meade, but certainly in other beers.
However, the main cause is a fining agent called Isinglass that is made from ground swim bladders of fish.
Some beer use animal by-products in their production. Guinness is popular example: isinglass, a swim bladder, is as a filter or fining agent.
In addition to the answers given above, some specialty beers include animal products as well. I have had beer made with oyster broth for example. That one is definitely not vegan.
Interestingly in the Middle Ages, they used to brew with chicken broth sometimes, and some other times with dairy products (including either milk or whey). That is worth remembering in terms of why some specialty beers include meat products as well.
As you might expect, it's all got to do with the ingredients. I'm a vegetarian myself, but not a vegan. So I do eat honey and dairy. With that said, some beers would not be considered vegan if they use those ingredients (milk stouts for instance use lactose).
However, an example of a non-vegetarian beer would be the oyster stout, which uses oysters in the brewing process.