I had a free service with only a tiny little bit of Adsense and some donations for 5 years. It was used by about 30,000 people over the lifespan with 5,500 active accounts at the time I announced that the free service would cost 0.99€ per month, starting in 30 days.
The goal with that pricing was to convert as many users as possible to the paid service. 0.99€ provokes this idea of "it's so cheap I don't even have to think about it" and it worked. In order to reduce the substantial transaction costs of such a cheap service, I offered prepaid accounts of 6 or 12 months, so the minimum transaction was about 6 euros and the fixed part of each PayPal transaction didn't grow too big. People who donated money before got 6 months for free. New signups get a free period of 30 days with no restrictions in the service.
About 80% of the users switched from free to paid, which is pretty good I think. However, I have to point out that my SaaS business is somewhat the best in its niche and there were no good free alternatives.
I doubled prices to 1.99€ euro per month last year and introduced a 3-month-prepaid interval. The increase in price was relatively well accepted. A few people complained, but I also offered existing customers to extend their accounts for the old rate, but only if they bought within 2 months. There weren't too many people who stopped using the service.
I can say that charging money and turning my side project into a serious business was the best thing I did in my life. In the Adsense times, I made maybe 400 euros a month, now I make close to 8,000 euro a month – same amount of weekly time investment on my side.
A very crucial thing that is often overlooked is that once you charge money, you turn your side-project into a serious business, which leads to entirely new situations you never thought of before. I get approached by people who want to cooperate. I see new opportunities for apps in the same niche. And I have a budget that can be reinvested to try things. If your site is just a side project, you'll probably miss many of these opportunities.
The only thing I wished I did differently was to start with the 1.99€ per month rate, since increasing prices isn't the easiest thing to do. 0.99€ helped to convert many people from free to paid, but it also set some boundaries in the perceived value of the service. After I went to 1.99€, people would say:"You increased the price by 100%." which sounds a lot more than saying "you charge a lousy euro more every month". I guess it takes a few years until I can start charging a bit more. Otherwise people would have the feeling that I double prices every year or so.
One more thing: I often heard that having a low-priced product is a bad idea because of the need to give customer support to a huge user base. I can't confirm that. I still get maybe a handful of emails per day and that's it.