If you plan to 'winterise' your boat, then fuel stabilizer is essential. Today's petrol/gasoline is far more 'cat-cracked' than it used to be (trying to extract every drop from the crude oil), and therefore tends to be more unstable than it was in the 'old days'.
There is a test for oxydation stability of petrol that every drop of EU petrol must pass, but often it is right on the limit, and it is tested ex-refinery, or ex-cargo. By the time it gets to your boat, it may well be several months later, and oxydation has already started.
I learnt the hard way, and I have had problems in the past with my chainsaws and with my boat.
It is better to do this than to drain the fuel completely, as stabilized fuel is better than humid air (IMHO).
(I used to be an oil trader for Total).