This article pinpoints some of the key problematic client types. Of course the list can go on from here, but it gives some good info as to what you should avoid and how to spot them.
My personal opinion is all clients should be taken on based on what the designer is willing/able to deal with. Though there are those very few perfect client/designer relationships, the majority will be problematic to a greater or lesser extent. Depending on the designer’s own experiences and people skills, they should judge what they feel would be a suitable client for them.
Remember, you pick your clients, they don’t necessarily pick you.
5 Bad Client Types Graphic Designers Must Avoid! at graphicdesignblog.org