I'm putting this post together to try to give you a window into my design preference. Other people's tastes may differ, which is certainly okay. I'm going to post a few pictures of stained and unstained woods. Hopefully it gives you a sense for some of the things that are out there, though I'm not really going to do the subject justice because there are literally woods of any color of the rainbow (orange, red, purple, white, and black among hundreds, if not thousands, more).
Lot's of pictures after the jump, some of which are kind of big. I'm not sure whether when google makes thumbnails of the pictures for in-text-viewing if it downloads the whole image (I'm inclined to think no), but if it does, then that would eat up 25ish MB-sized chunk of your mobile data. If you open the images separately however, I'm sure it would load a large image. So proceed informed.
Here is a piece of red oak that has not been stained, but has had a clear satin varnish (only one coat because I'm in the process of finishing it completely) applied to it:
It's generally light in color with a slight reddish hue. The grain pattern is visible and distinctive without being extremely prominent.
Here is a piece of red oak that has been stained with Watco Quart Dark Walnut Danish Oil Wood Finish (seriously though, this name is really misleading, it ends up looking nothing like walnut):
The stain accentuates the grain pattern and changes the wood's color from its natural light but slightly reddish color to one that is a darker, golden-tannish, brown.
Here is a piece of Honduran mahogany that hasn't been stained, but has a clear gloss polyurethane finish applied to it that I've polished:
The grain pattern is tight and not very prominent (that is a good point of contrast between it and red oak and not really a feature of differences in finish). Its color is naturally this warm golden brown, with an emphasis on the golden warmth in its color profile. Its natural color is not too far removed from what we achieved with the stained red oak. Nature was kind enough to grow a tree somewhere on a Caribbean island that naturally has the color we used stain to achieve. Admittedly, Honduran mahogany is about five times as expensive as red oak, so I can see the cost-conscious reasons to opt for stain.
I don't have any stained mahogany because the whole reason you pay for mahogany is for its color. It sort of defeats the purpose to stain it.
Here is a comparison picture of the first three I put up side-by-side:
To show a darker wood, here is a piece of walnut, no stain, just a polyurethane finish:
All I'm going to say about this one is that it shows an example of a naturally dark color. Like mahogany, it is more expensive than red oak (about double).
Lastly, here is a comparison picture of all four side-by-side:
At the end of the day, do what you like, and use the materials and finishes you like so you have pieces you love. If that means stain, then go with stain. If it means no stain (as is often the case for me), then go with no stain.