Why do we itch? What purpose does it serve, evolutionarily speaking? It’s not like pain, which is signaling something is wrong and/or injured; it seems to me to be nothing more than an annoyance. For the life of me, I can think of no good reason why we itch. If we didn’t itch, would we be any worse off?
There’s a bug on you.
Huh? 
Well, you’d scratch if you got an itching sensation brought on by a little creepy-crawly thing that might carry disease, right?
As in:
it’s probably not good to have bugs on you ->
having bugs on you make you itch ->
you itch ->
bugs fall off ->
you are better off than one who didn’t itch who dies from disease carrying bugs and you therefore procreate while they didn’t
It doesn’t have to have a “purpose”; it just has to be not disadvantageous long enough to interfere with reproducing successfully.
Itching can also indicate an allergic reaction, like if you eat something you’re allergic to or brush up against an irritating plant. Better to get an early warning of an itch, rather than have to wait after more exposure for something like full-on anaphylactic shock, etc.
Itching serves as a clue that something is going on with one’s skin and underlying tissue. Whether it’s an insect, prolonged pressure or humidity changes, or exposures to environments or chemicals which are altering the skin without triggering pain receptors, a clue is sent out to do something about the situation.
I recall reading some time ago that itching appears to be something that the body does with low levels of pain to get your attention, such as pointed out above the pain caused by an insect bite. Tickling being the equivalent mechanism for low levels of touch (such as the pressure of insect legs on your skin). In both cases you pay attention to a stimulus that otherwise would be too weak to gain your notice.
Nothing has an evolutionary purpose. Evolution is the result of random mutations - some of which stick around. Mutations that have great benefits are likely to hang around, while those with great detriments are not. But there’s no purpose - our species didn’t decide that ithcing would be cool and then develop it. A lot of what goes on does so because it was a side effect of something else - or the resultant side effect of millions of other things.
Okay, maybe a poor choice of words. Let’s say instead that there are evolved traits that have a benefit.
Some yes, but not necessarily all (but you probably knew that).
I think this is a very early evolutionary development. Even fish will scratch themselves by rubbing against objects. It’s just response to stimulus. The stimulus may seem to be a stray one sometimes, but that’s because we have sensitive senses, and they will react to things we can’t otherwise identify. So when you feel an itch, it is something. Excessive scratching is likely to cause skin irritation and sensations that will continue the activity, so even people who seem to scratch themselves compulsively probably have real sensations triggering the urge to scratch after the initial scratching.
But the “itch” brought on by “creepy-crawly” things is typically after you’ve been bitten or scratched by one. Again, what benefit does the itch itself provide?
The sensation of having a bug crawling on one’s body is not the same as an itch resulting from said bug biting or otherwise inflaming one’s skin.
One benefit of an itch is that it encourages you to avoid getting bitten by insects and insects can carry diseases.
Ahhh, I didn’t think of that. Getting bitten and not enjoying it, and subsequently taking action to avoid getting bit again. Simple, yet over my head. 
And it helps prevent you from being bitten again and again by the same bug.
This is false. The theory of evolution explains how organic entities come to have purposes despite the fact that there is no agent to intend these purposes.
You seem to be talking about the same thing. There’s no intended purpose, but there is a purpose is served, sometimes.
Now seeing as how we are talking about stimulus response here, I’d say the resulting purpose is to interact with the environment.
I think we’re just using the word “purpose” differently - I was referring to the word in its sense related to “plan” (see 2) while you seem to be referring to its meaning closer to the word “function” (see 5). Both are related to 1, but in this context the use of “exists” or “is done” changes in the meaning of the first definition quite a bit, with the connotations being along the lines of the differences between 2 and 5.
You’re probably thinking of mainly of mosquito and fly bites, which bite once and then fly away. But in our evolutionary history ectoparasites like lice, ticks, and fleas were more important. These take up residence for awhile, and the itch produced by a bite prompts you to hunt for the bugger and also his companions.
Ticks are common in the forests where I work in Panama (although they fortunately don’t carry disease here). Many times I’ve found a tick in an obscure place because of the itch, and removed it before it had completed its blood meal.
The itch sensation undoubtedly evolved so that we would remove irritants like ectoparasites from the skin, or avoid stinging plants, etc. But it is sensitive enough so that it is sometimes triggered by other things that are not dangerous; this is an “unintended” side effect.