It is well known that smoking increases both the severity and frequency of flares in people with Crohn's disease. What is not clear is whether that is due to the nicotine or the thousands of other toxins in cigarette smoke. A cursory search only returns studies which show that smoking cigarettes makes Crohn's worse. I can't find any studies on the topic of whether alternative nicotine delivery methods (such as e-cigarettes) makes Crohn's worse, but if anyone can find some then that would form part of an ideal answer.
As a side note, we know that nicotine tends to actually improve symptoms in Ulcerative Colitis, the other form of inflammatory bowel disease. We know in this disease that this is due to the nicotine and not the other toxins in cigarette smoke, because there are plenty of studies (for UC only) that can be easily found linking the use of nicotine patches to an improvement in symptoms.
Note: Even though I have already accepted an answer for this question, new studies are done all the time and I would be highly interested in and upvote any other answers that are added which contain more studies on this topic.