Paypal is amazing for this. I jump between trials for news outlets and I can just sign up for the trial, immediately cancel my billing agreement through Paypal's interface and when the service tries to renew they'll simply be denied. I'm not sure if even possible for them to check, but services only seem to notice when they try to charge me again.

Once pitfall is you should never attach a credit card to a service you do this with. Back when I was a student and I re-instated my Chegg subscription with a credit card to study for finals and they immediately back-charged me for the time in between. This was despite being pretty certain I also cancelled from their website, and 100% certain that they had cut off my service for that time period, otherwise I wouldn't have been prompted to renew my subscription.

After a long phone conversation I learned companies don't care about well-reasoned arguments, but they'll flinch at the first mention of a charge back.