Web Webster + 1 for starting from the beginning. Stephen Maturin's character is revealed in minute brush strokes throughout the series; the first 5 books are essential (IMHO) in establishing Maturin's essentially dour outlook on humanity and help you understand how his background led him to become the weirdly engaging crank that he is.
Christopher Taylor You can read any of the books as is, but I recommend strongly starting at the beginning.
Jon I started at the beginning, so I can't answer for what lies ahead. But I will tell you the first few in the series are very enjoyable, and do give quite a bit of background to situations alluded to in this book. This one seems the most sure-footed of the series so far. I would say go back, but only for more character building and background (O'Brian does pretty well with catching a new reader up I noticed).
Debbie Higgins Start from the beginning. O'Brien writes in the style of the period and you need to get used to it. Also, this does flow from book to book. But they are worth every bit of it. History, battles, luck, humor. Great series. You'll miss some great stories if you don't read the first ones.