When approaching an essay, I try to do two things with the start of my introductory paragraph. First, in content I aim to provide context for the eventual thesis I provide. I ask myself, "What is the larger conversation or issue that my thesis relates too?" I then seek to answer this question and so start off by situating my reader in the larger discussion and preparing them for my specific contribution to it. Second, I try to make the opening sentence interesting. For example, if writing a paper on underage drinking, one might start off by citing a gripping statistic or general fact about underage drinking, such as, "One of the most difficult challenges facing California universities today is how to deter underage drinking." This opening sentence meets both of these conditions: it provides a broad issue which then a thesis about responding to the problem of underage drinking in universities can address, and it also "catches" the reader with its provocative and alarming style.
It is certainly a good idea to utilize an introductory sentence to captivate the reader. However, I warn against using "truisms" or "no-duh statements." For example, if you are writing a paper on traffic accidents in the United States, don't begin by saying "traffic accidents are very bad." That statement, though true, has little value. When trying to start a paragraph this is your best opportunity to be creative. Think of something interesting, captivating or that adds a little bit of flair to a mostly dry and informational essay. Of course, this should be done in a serious manner (I would avoid jokes), but you can still have fun with it.
I like opening my essays with a short anecdote or a personal story and then slowly zoom out into a larger issue - introduce the main argument for the paper (which will have a connection to my personal story) and finish up your intro with a thesis statement. I think it is an effective way to start an essay (especially a persuasive essay) as you can grab readers' attention right away and make them want to read the whole paper.