Just curious.
Karl Rove?
Seriously, I think it’s tough to attach standard models of animal intelligence to insects. They just work so differently. Responding uniquely to new challenges in their environment is just not in their repertoire. Would you accept the definition of “most complexly programmed” insect?
But if you want to stick with your original proposition, I would have to conclude that the answer is the spelling bee.
Or the sav-ant, maybe?
My vote is for the spider.
You try making a web.
If we’re talking about the relative complexity of their mindless behaviour, I think termites’ architectual achievements trump spiderwebs. (Leaving aside that spiders aren’t insects.) 
:smack: yeah, you’re right technically. I guess the holiday spirit has me thinking about spiders.
However…they definitely fall into the bug category. 
If spiders don’t count, then I’m gonna go with a honey bee.
I was thinking spider mainly because it builds the intricate webs alone. Rather than say…thousands or millions of insects working together. Which could be used as an argument also. Size was also a consideration…not that “brain size” is a reliable indicator of intelligence but there is a correlation.
Damned houseflies and the way they seem to bug you on purpose and land where you can’t quite get them.
How about the cockroach…he’s managed to survive the longest. Gotta be some evolution in intelligence there somewhere.
IANAEntomologist but the OP could probably branch in to both most “intelligent” individual insect and most robust insect group emergent behaviour(i.e group intelligence)
For “intelligent” as normally defined and understood, you might as well ask “What’s the most intelligent rock?” The concept doesn’t apply to anything we know about insects.
I seem to recall reading that honeybees are more intelligent than (I think) houseflies, in at least certain circumstances. Apparently, both were taken aboard the Space Shuttle, certainly a situation for which neither’s evolution prepared it. Neither was able to fly properly in its accustomed fashion in zero gravity, but the bees (and not the flies) were able to learn a new set of wing motions which were effective.
Bees are also relatively easy to train, via standard conditioning methods. I’ve seen some work, apparently very successful, on training them to find landmines. And they also show a level of communication unmatched by most other insect species, in “dancing” directions to flowers. So all in all, I’m going to go with the honeybee as most intelligent insect.
I believe the question was a insect,plural?
A honey bee would’nt be close to that by itself,maybe the hive,yes.
I read an artical a ways back about the Dung bettle,it actually uses shit from other animals to lure their pray to them,dont remember which pray it was.But some insect guy decided to take all the piles of shit away from around there burrows.The bettles went back out to collect more,bring it back,and start over.Any bug that goes to that lenth to roll some shit from who knows where,back to home,deserves a second thought.
Dung Bettle 
I’d have to go with Africanized killer bees, cause they kick the honey bees asses and take over. That makes them smarter, right?
According to this expert , man is the most intelligent insect.
Carpenter ants and carpenter bees. I think the ants are with the Teamsters…don’t know what union represents the bees. These suckers will work around the clock. There is a Mexican contingent that works just as hard, but, you have to keep your eye on them.
I’m surprised nobody has mentioned fleas. There have been countless fleas that have been trained to perform in flea circuses throughout the ages. 
What?
My wife insists it’s the Lady Bug.
Plus half-bees make lovely pets!
I vote for the Portia spider. OK, so it’s not an insect, but it’s still an arthopod.
The brain bugs, natch. They kicked humanity’s ass at Klendathu.