Why is email free to us? Do they recover costs and make profits through ads? Or is it a long term strategy to make us too much dependent on emails and then make it a paid service?

A good rule to keep in mind on the Internet is that if you aren't paying for the product or service, you are probably the product.

Yes, it depends completely on the specific site.  Many are indeed funded through ads.  Some do expect to move to a paid subscription eventually.  More are likely to offer a 'freemium' model, where the basic function is free, but when you want enhanced services, you have to pay. And a few very misguided souls are still operating under the idea that having subscribers and traffic is a good thing and that someday they'll figure out how to monetize it.  That's not a sustainable business model.

One hugely important factor here is simply business and competition. If Google were to suddenly charge for using Gmail, you would be free to leave and use another service instead and Google wouldn't benefit from that. How you might ask, since it looks like Google is giving something to you completely free of charge - and they are, you're not paying anything, but they're still making money from your activity. If you paid 50 USD a month for a dedicated server, that could potentially serve 3000 people giving each person 2 GB mail storage - so the total monthly cost could be below 2 cent per user. Now that number could be completely different, but it is not unrealistic in any way. When you log in to your Gmail and read a mail from a friend concerning some new super cool loudspeakers, you might see an ad promoting some company called Clear Sound, and guess what, they sell loudspeakers. If you click that ad Google is likely to receive maybe 50 cent from whoever created that ad. Some ads will pay less, some will pay more. But the point is that just a few clicks on ads could be enough for Google to provide you with Gmail for several years.