The first site I found while I was looking for an open problem was Open Problem Garden. There you can find many open problems in different fields of Mathematics. I was looking for a problem in graph theory and so I found the Cycle Double Cover Conjecture. I like the simple formulation of this conjecture, but there is a lot to tell about it.
In the 1970's Szekeres and Seymour formulated the Cycle Double Cover Conjecture independently. Today, it is one of the most important open problems in Graph Theory. While trying to prove this conjecture, other stronger conjectures were found. I will give some more information about some of these conjecturesunder the tab Stronger conjectures . The conjecture has been proven for some special cases, which will be listed under the tab What's known. Some of the concepts used at this website are explained under the tab Concepts.
The main ideas come from the website named above, some of the articles that are named there are included under the tab What's known. Besides the website, I found the book Circuit Double Cover of Graphs by Cun-Quan Zhang (London Mathematical Society Lecture Note Series: 399) very helpful. I will refer to this book by [Zhang].