I'm trying to remember which older game had 3 dimensional stars. In fact, while the galactic disk is indeed pancake shaped, it does have a fair amount of 'girth' along that disk. which is why when you look in the sky, you see stars in all directions, not just say along the equator. Of course, if you are away from light pollution, you can also make out the Milky Way as a band crossing the sky.
I just remembered, Ascendency has a 3d star grid, with set warp lines/links. You can rotate the star grid in 3 dimensions to get a better view of your own empire, etc. This could get tricky sometimes, if a star was showing in front of/behind a link, hence 'fooling' you into thinking it was connected to that link when in fact it was some distance away from that path between two systems.
That being said, while it would be cool, it doesn't really add a whole lot to gameplay, especially where fleets don't form 'battle lines' in GalCiv due to the vastness involved. The 2D star plane adds enough elements for now, and I'd rather see the designers focusing on other things, like new cool techs and such.
If we had a LOT more fleets, then you could spread them out to protect all of your borders, but essentially we move fleets to intercept, or leave them near a planet to defend, but open space is too vast to make a 'long defensive line' truly practical from all directions, unless you have only one or a couple of star systems colonized.
As for how you make a 'hex grid' 3d, it is possible, when you think in terms of triangles instead of hexes. Essentially, the next 'layer' up is offset from the original grid by 'half a hex', and so on. A better way to visualize this is to think of the hex grid as points layed out in a hexagonal pattern, not physical six sided shapes. So from one point, you have six points you can move to Similarly, From that central point you will have a number of points upwards and downwards you can move to. I'm visualizing 3 up, 3 down, so you have 12 options for movment.
Really though, if you are going 3d, ya might as well lose the grid, and just go with distances. Of course, how you'd visualize an object's orientation on the Z plane is an interesting problem in of itself.