Most mid to high level mountain groupsets (eg SLX and X7) have shifter options without any display as to what gear is currently active. How do riders avoid cross-chaining and other unpleasantnesses, especially when riding in the dark or on rough terrain (i.e. when they can't readily take a look at the rear cogs)?
All the elite riders I have encountered just know. I think its part of the attention to detail necessary at that level. You almost never see them looking down to check (that would be showing a weakness and giving oponents an opportunity).
But if you mean can the rider say which cog they are using at the front and rear? then the answer is that often we can't say.
Usually we know by memory which front cog we are using. And as I change the rear gear, I know by the different feel of the ratio whether I'm near the top, the middle, or the bottom of the cluster. I very rarely try to change gears past the last one.
The bike knows. That's enough.
One of my bikes has no indicators and I'm less familiar with it than my other bike which has indicators and more years especially at the top. But I don't find it to be a problem. You don't need to know exactly which gear you're in, just enough to know (e.g) that if you want to drop a gear you need to drop a chainring. A combination of feel and a vague recollection of what I've done is normally enough for that.
I consider myself decently experienced, having ridden for many years, and my answer is that I don't have to know. The numbers aren't important to me; it's all in how it feels. Whatever speed I'm going, if I want to go faster and I'm pedaling without feeling like I'm doing any work, I need to shift into a higher gear. If I feel like I'm expending too much energy (i.e. it's too hard to pedal), then I gear down. There's not a "right" gear to be in; it's relative to my current speed and how much work I feel like doing, or, in some cases, how much torque I need.
A lot of the time I don't…
Most of my riding is on an older touring bike with downtube shifters or a tandem with mountain bike type (the two button/lever kind) shifters. So I know generally what gear the bike is in by effort and like Michael says detect cross-chaining by sound. With the touring bike shifter position tells me a lot about what gear I'm in and I can read it by feel. On the tandem I can tell the extremes by the shifter behavior (it either won't let you pull cable or won't release anymore).
I also have a pretty relaxed attitude towards cross-chaining. I know it is "bad" and try to avoid it, but I also don't worry too much about occasionally picking the "wrong" gear combinations. I usually notice them due to noise or feel and when I do I shift if I can. If I can't a put a bit of money into the bike parts jar when I get home.
With todays 2- and 1-chainring cranksets, chain-crossing isn't a problem and with the cranksets where it may be a problem (which are rather rare in high-end groups) the sound and feel are good signs of it. So you don't really need to know which gear you're in.
And when you spend a lot of time on your bike you just start to recognise the gears by feel and are able to tell which one you're in... well, +/-1 let's say.
I switched from Shimano Deore (with displays) to Sram X9 (without displays) some 5 years ago, and never felt the need to look down and check the gears. So they are not this important, just a matter of changing habbits.