What exactly is the point of keeping up with the specific gravity of your beer? Other than knowing when primary fermentation has ended?
The difference between the specific gravity of a beer at the start of fermentation (OG) and the specific gravity at the end of fermentation (FG) gives a measure of the alcohol content of the beer. A high OG also gives you a measure of the potential alcohol that can be obtained in fermentation.
The most important benefit of taking gravity reads in my opinion is neither for determination of ABV or fermentation completion. Taking gravity readings gives the brewer an idea how much in control their process is and aids in future brewing repeatability. This is of specific benefit to all grain brewers due to the increase variability inherent with sugar extraction process of the raw grains and alternatively lesser benefit to extract brewers.
http://www.beeradvocate.com/community/threads/help-me-care-about-gravity-readings.204599/ Gravity readings are essentially data points that you can use to evaluate a huge portion of your brewing process, adjust your product, brew to style, and improve your ability to reproduce good batches / improve consistency. preboil gravity: (combined with preboil volume) - can tell you how much sugar you have extracted from your grain which helps you judge the efficiency of your mashing / lautering process, sends up a red flag (when low) that points you in the direction of what to focus on for improving it, and (when consistent) helps you create future recipes so that you are more likely to execute your beer as designed / intended. original gravity: (combined with postboil volume) - can tell you more about your boil off rate and, most importantly, acts as a baseline measurement that will later tell you how well your yeast fermented your beer and how much alcohol is in your final product (when compared to final gravity) specific gravity readings during fermentation: - can be used to judge the rate of fermentation which can be an indicator of yeast health, whether your pitch rate is proper, whether your fermentation temperature profile needs to be adjusted, can also help you really understand the different behaviors and preferences of various strains of yeast you choose to ferment with. final gravity: - needed to determine how well your yeast attenuated your batch, can serve as a general benchmark for the sweetness vs. dryness of your beer (although perception can be different), can be used in decisions to increase, decrease, or keep your mash temperature the same next time you repeat the batch, can be used to determine that fermentation is actually complete which helps you avoid bottling too early and having your bottles explode, etc.