The Paradox Interactive games (Europa Universalis I, II, III, Crusader Kings, Victoria, Hearts of Iron I, II) are brilliant 4X games, but have a ridiculous steep learning curve. A bit too abstract for the most gamers, but if you manage to understand it, it's really really addicting.
Civilization is the king of 4X in my book. A very appealing idea of guiding your little tribe through time with simple effective diplomacy and the thrills of an escalating nuclear war.
Master of Magic was a brilliant Civilization I clone set in an fantasy setting. Loved it. Age of Wonders is quite nice in that aspect as well.
In space, it's Galactic Civilization I and II all the way, though closely followed by Masters of Orion I and II, Ascendancy and more recently Sins of a Solar Empire.
For a little more onscreen action, it's the Total War series for you, because, and only because, of the massive RTS battles. Though it's not Civilization with added RTS battles. With the RTS stripped, it's an average game series.
Stretching the envelope a bit; Jagged Alliance and X-Com. More a squad-based 4X.