As @jgaiser said, the Patrick O'Brian series is excellent (his writing improves throughout the series)...
In the same approximate time period:
-Richard Woodman's
Nathaniel Drinkwater series is quite good (though I didn't care for the rest of his works)
-Dewey Lambdin's
Alan Lewrie series is very good with a flawed and somewhat humerous main character (this series is ongoing still)
In the same time but different genre (Non-Naval)-
-Allan Mallinson's
Matthew Hervey series about a British Cavalry officer in the Light Dragoons from the Napoleonic Wars through India and South Africa is well done.
-Bernard Cornwell's Richard Sharpe series is a classic from the perspective of a foot soldier during the Napoleonic War mostly set in Spain and Portugal
An Identical thread was started a while ago...you might check it out (
here)