Your own email account on a VPS or other web hosting? I've been doing this for my work email for years, moved my personal email over at the start of the year and so far it's worked perfectly. Thunderbird's support for long email threads isn't as good as Gmail's but that's about the only downside I've seen (and that's a downside of Thunderbird, not of the approach to email).
No, really. even though free accounts ending. Actually not even sure if you can sign up at the moment. Has basically 'just worked' for years though, hopefully they stay in business. :/