To be clear: Mailgun is still free for 625 emails per month - they don’t bill for any charges less than $0.50.
Whether you’re sending more or less than 625 emails a month, Mailgun still works out cheaper and more convenient than pretty much any other option mentioned here.
If you want to optimise for quality, most of the other products mentioned in this topic are far superior. But for people reading this trying to optimise for cost: The cheapest/free option which makes most sense for most people is still Mailgun.
Direct quote from Mailgun customer notification:
On March 1, 2020, we will automatically transition your account to the new Flex plan, a pay-as-you-go plan comparable to the Concept plan you’re currently on. You’ll receive your first invoice under the new plan on April 1 if your amount due is greater than $0.50.