Diagrams alone are not always helpful. For example, the use case diagram can't convey business rules in detail. The class diagram may be very useful since you may be able to generate class code and DLLs from it.
I find these diagrams the most useful:
- Use Case Diagram
- Class Diagrams
- Activity Diagram
- Sequence Diagram
There are so many useful resources, but check these:
- UML End-to-End From Use Case to Sequence Diagram - Essential Software Tutorial on YouTube
- "Practical UML: A Hands-On Introduction for Developers" by Randy Miller
- Sparx System's UML Tutorial
- OMG's UML.org
Edit-1 in response to Mark's comment.
While I don't use these resources day-to-day, they serve as quick reference for UML syntax. The above resources are chosen since they provide quick and somewhat comprehensive representation of UML diagrams. It shows common diagrams and helps the new UML user quickly see the difference between them. The first resource, the video, gives details about the Use Case and how it relates to other diagrams. The above resources are not expected to be enough for anyone who wants to learn UML or OOD, I realize that learning such topics was not intended in the original question.