Do tent colors have functional purposes?

Just to sum up other answers and add something that was missing:

• As mentioned choose surrounding nature color if you want to blend in (e.g. while wild camping where it is not legal). Green, brown, grey or white depending on the place you camp.
• Choose bright color for emergency (valid reason) or ease of finding your own camp (not so valid, don't be so careless to lose sight of your camp). Orange works best.
• Insects. While most animals won't be bothered by any color, some colors tend to attract insects. E.g. yellow Nemo Hornet Elite can be a nightmare with some type of insects.
• Temperature. Dark can get hot in midday, bright is nice early in the morning (though might have only psychological element if camping in cold areas).
• Light hue. If you're spending more time inside the tent not sleeping (e.g. caught in heavy rain), orange hue (Big agnes copper spur) is not the best if you are trying to read a book/kindle. MSR Hubba Hubba tents with grey is best for reading, very bright and natural light. Dark colors (dark green) is only suitable for sleeping, light green (any Nemo tent with birch green color) is ok to spend time inside as it tends to have little hue to the light.
• Depression/Melancholy. I forgot about this at all when posting first as it doesn't affect me, but there is actual people who reported emotional problems during prolonged stays in the green tents. Solution for depressed ones is lightweight MSR tents with euro green fly which is dark olive color. This particular color doesn't create any green hue, furthermore fabric is thin, therefore it is only dark from outside and bright inside.

I personally like to blend in well and usually hike in grassy areas, so I prefer greenish tone tent with orange footprint (in case of emergency). Light grey is close second for that bright and natural feeling inside.

From my experience, other than emergency situations and getting lost, there are three differences the colour of your tent can make:

• A darker colour will get hotter in the sun than a lighter one (usually)
• If you're at a busy campsite, many people will have a green tent, but grey and orange are less common colour choices. This will make it easier to spot your tent from across the campsite.
• Brighter colours will attract more insects, which is slightly annoying.

Depending on where you camp most often you may want a different colour

In addition to the advantages of being easily spotted or easily hidden, and to elaborate on previous answers - specific colours can attract specific insects which may be relevant to where you're camping.

For example, the Tsetse fly is attracted to a mixture of black and dark blue colours. So if you're planning to camp where they are endemic then consider other choices - bearing in mind the other fauna that alternative colours may attract.

Personally I want to be as unobtrusive in the wilderness as possible. There seems to be a lot of focus on, even fanatical devotion to, leave no trace. While bright colors aren't technically leaving a trace once you take the tent down, you are unnecessarily polluting the view of anyone else that happens to be there. It's kindof like jumping up and down shouting "Here I am, here I am.".

Most of the time, being unobtrusive is merely being polite to others, but there can be times it really matters. One obvious case is stealth camping. In places where the land is tightly controlled, like New England, it's not always easy to find a clearly legal place to camp. Sometimes the best alternative is to go a few 100 feet into a patch of woods, be as unobtrusive as possible, and of course have as little impact as possible.

Theft or other illegal activity is another, although admittedly minor, issue. One time I was swimming with some friends in a lake by the side of the trail. We put our packs down by the edge of the water. When we got back, one of my friends' pack was gone, and another one had been rifled thru. Mine was completely untouched only about 2 meters away. The only difference appeared to be that mine was olive gray-green, and the others were bright colors. It seems the thieves simply didn't notice my pack.

I'm currently looking to replace a small backpacking tent that got lost in airplane luggage last summer. I'm very dismayed by the many options that only come in bright obtrusive colors. Those are non-starters for me. Fortunately some companies get it and either offer a color choice or a single more muted color.

If you want to reduce your visual impact on the other people in the area, choose a tent with colors that match the landscape you're going to camp in. Green in forest or other vegetated areas, brown for the desert, white for winter camping.

However, if you are in trouble and want to be found, it helps to have a very bright tent that stands out. A tent you can see from kilometers away. A tent that is going to annoy that other backpacker who was just having the illusion to be alone in the world, and now he or she isn't. Such a tent might save your life if rescue agencies are looking for you.

So, to reduce visual impact: choose camouflage. To quicken rescue in emergency: choose anything BUT camouflage.

If you are stealth camping, it helps to have a tent that blends in. If you are camping where there is hunting, it helps to have a tent with bright, high contrast so that you can be sure you are seen.

Also (thanks to Ben Crowell for the comment) you may want tents that blend in for high traffic areas to disturb the scenery less. High contrast tents can be useful in the backcountry to make it easier to spot your tent.

That being said, I've never considered color in tent purchases.

The hue of the tent colour can also affect whether insects and flies are attracted to the tent.

In some cases certain flies like certain gaudy colours.

However more commonly it will be flies that shelter in darker hollows and under grass and leaves that will like the dark tent, while a lighter shade may make those flies swarm above their normal dark foliage (this is with a 'green' tent).

In Scotland this can be the case for midges which can ruin an otherwise wonderful campsite when the air is still and the sky is overcast. The (biting female who desire a blood meal for mating) midges will congregate in the lee of the tent, and if it's quite dark may even crawl over the tent outer. This can be bad when entering and exiting the tent as they brush onto you, the victim...

Light colours don't heat up as much during the day, nor cool off as much at night. Light colours allow more light in the tent. If I'm stormbound I'd much rather be in a white/light beige tent than in either red or green.

I have a Marmot tent and those were my color choices. I chose the brighter one as I thought it would be useful if I were lost and needed visibility, either lost from my own campsite or in need of rescue, and because orange seemed more cheerful.

I discovered that the light gray and orange fabrics let through more morning light than olive drab tents I have seen to compare to (not exactly the same tent however). This may be useful in waking up early and/or seeing to get dressed, but it can also cut short my sleep as with a more opaque fly I could sleep until the tent started warming up. Now I know I need to bring a sleep blindfold if I intend to sleep in.

Most things have already said, the only item I couldn't find is that if there is a multi-color pattern on it, it might be slightly easier to set up the tent (especially when each side has its own color); this mainly applies when the tent is big.

Also, a lighter tent is easier to setup in the dark if you don't want to use light, because a light surface reflects light better (e.g. due to mosquitoes or other reasons).