Okay, so I guess the word is a "mercator projection" and this link is perfect! I was actually trying to put a loop closer to the pole just to minimize the artifacts at the top, but I couldn't get it to work. I will update with a picture:

http://blender.stackexchange.com/questions/3315/how-to-get-perfect-uv-sphere-mercator-projection

Edit: I am getting a flat unwrap, but I am still getting a seam, but that is mainly because the images I am using are not seamless. So I guess this helps with the dome at least, perhaps this "follow active quads" feature of Blender will help a little.

By the way, I started with a full sphere, and after I followed the steps in the link above, I deleted the bottom half of the sphere.

Thanks JT! I am all for avoiding UV unwrapping. I will check out Cube World indeed. And I will look into tri-planar texturing. I sort-of got something workable from the method I mentioned above. Here is a screenshot of the level:

Edit: That Cube World game gives me a good idea!

Avoiding seems with UV mapping often takes skill in 2D image manipulation software. Using the same texture element on both sides of the UV seem allows the artist to align the surface parts in the UV map viewer. Usually it is possible to make the seem invisible.

UV unwrapping is, indeed, a tedious task. I don't really have anything to add to the discussion to make it easier, since I struggle with it myself even after all these years.

However, I would like to just throw a suggestion out there. How about eliminating UV unwrapping entirely? Depending on the style you are shooting for, it is entirely possible that you can make do with entirely procedural coloration/texturing, rather than texture mapping. Look at games like Cube World, which has minimal (if any) texturing, and relies almost entirely on coloration and AO to provide the rich visual appearance. On the other end of things, if you want more visual detail than simple vertex coloration, you can use techniques such as tri-planar texturing for terrain and landscape objects, and with some creativity, it can be used for all sorts of things.

Granted, doing procedural coloration and texturing moves work required from UV unwrapping over to additional shader creation, but for a programmer it can be a worthy trade.

Procedural baking of textures has much room for improvement, so expect progress there in coming years. Eventually software will easily take point data and associate it with locations on the texture to automatically align 3D surfaces with those points, thus eliminating the seems. The 3D theory is in discussion about micro pixels and also connecting 3D coordinates more closely with 2D texture coordinates. However, with current computer rasterizing, this is complicated and unreliable at present. Even with progress down the road, I expect that some manual unwrapping and making the associates between 2D and 3D in the UV map viewer to be needed for a long time to come.

Of course, nothing now beats taking a high density image and applying it to surfaces for an exact representation of what was photographed. Complicated surfaces will in this case still need UV map work, so tedious UV map work for complex surfaces is here to stay for a while, isn't it?

After watching the above series, I feel MUCH more confident tackling UV unwrapping. The one thing he said that helped me understand how to mark seams was that it is just like using scissors to cut through a piece of fabric.

So I imagine the object as a piece of fabric that comes loose where I cut it. I imagine all continuous faces as a continuous piece of fabric.

I was able to unwrap a cube with ease!

As a note, I used "Follow Active Quads" as the unwrapping procedure.

With just one small cut from the north pole to the equator of one loop of the sphere, and selecting the face adjacent to the two meridians, and then selecting all, and choosing "Follow active quads" I was able to get a good uv unwrap on this sphere:

This still has bad seams, but I will get it eventually. Anyhow. Good thread!

Just so you know the potential, I have on rare occasion cut and unwrapped objects with very many polygons and dozens of cuts. A model of a particular ship hull that I created a couple years ago (approved for use in a game) took a whole day to UV map, but when I was done it had no seems and no distortion in the texture mapping. Another model had about 120,000 polygons, hundreds of individual objects, and several textures to be mapped, which took about two weeks to UV map. People say it looks awesome like its real. It is in a simulator.

So, since all 3D modelers start like you, then appreciate the huge potential you have in this art form.

Keep having fun and work hard at it!

So, have you ever dreamed in 2D? I know it sounds weird, but I seriously had a dream that was in the style of paper cutouts. Haha.

Yeah, once in a while after spending a lot of time with the 2D aspects, that night I might have a dream or two about all this.