Galactic Civilizations III is quite good, as is Pandora: First Contact.
Some put Sins of a Solar Empire into the 4X category, I myself do even though it is real time strategy.
I don't have a recommendation:
But...
Distant Worlds: Universe - Avoid this 4x game. Because the game is too large to micro manage, and the AI does a craptastic job with anything called strategy. I played for maybe 30 hours before giving up in frustration. Some people swear by this title, but understand, the strategy is broken. If you automate your fleets. They randomly ping pong against enemy colonies while leaving your empire undefended and just suicide themselves over and over again. There is nothing you can do to prevent it with any automation.
Endless Legends (Metacritic) has really surprised me. I haven't gotten very deep into it (maybe 5 hours gametime), but it's exceedingly beautiful, UI is excellent, and seems to have a huge amount of depth. I got it from GMG for 25% off with the code going around.
Everything in this thread so far is a good rec. Also, Civ:BE is out in a month so keep your eye on that.
Age of Wonders III is quite good, surprised no one has mentioned it yet.
Galactic Civilizations III is quite good, as is Pandora: First Contact. Some put Sins of a Solar Empire into the 4X category, I myself do even though it is real time strategy.
Sword of the Stars is Great, SWOTS 2 even with patches is still lacking, not up to par with SWOTS 1 IMHO.
Just because there's lots of TBS 4x doesn't mean it's a requirement of the genre. There's plenty of old and new examples of RTS/pause ones some bad some decent/good and such.
I'm not really sure Sins in particular truly qualifies. It has everything there in name, but it really plays way more like a traditional RTS than other 4x games.
I liked Endless Space. Endless Legend? I'm not sure about it. I've played it for a couple of hours and I have mixed feelings. My friend absolutely loves it though.