I've brewed a good dozen batches of beer from kits, extract, extract+grain, and now all-grain, and I've never measured gravities. Why measure gravity, besides to know what you're getting? Is there any advantage to putting the beer in the secondary as soon as the measured gravity has finalized, instead of just guessing observing that the fermentation is done? Any other reasons?
If brewing all-grain, taking gravity readings after mashing allows you to calculate your mash efficiency. If your efficiency is low (meaning you're not getting good conversion), you can use this knowledge to pin down problems in your recipe, milling, and mash/sparge processes.
Measuring the gravity before and after fermentation allows you to calculate the amount of alcohol in your beer.
Taking multiple gravity measurements near the end of fermentation allow you to verify that primary fermentation is complete. Airlock activity alone is not enough. This is especially important when bottling as an incomplete primary fermentation greatly increases the risk of bottle bombs.
Using a beer thief and hydrometer makes you feel like a mad scientist and impresses your friends.
I have brewed many batches where I never checked the gravity in the past. You don't really need to check the gravities to make great beer. You do run the risk of not knowing when a beer is complete and maybe having overcarbonation issues in the bottle. But good fermentation practices should, normally, take care of that.
However, I think that when you get past just wanting to make beer to drink and you really want to start nailing down a great recipe; gravity measurements are part of many different data points to collect. Getting those #s help you to hone in on potential issues. And they also help you monitor consistency batch to batch. A solid process in the brew house yields the ability to build better beer because you are consistent.