My next door neighbor has run his black corrugated pipe from his
downspouts down to the back corner of our adjoining lot, right up the
the fence, and it is draining directly onto my property, and drenching
the footings of my shed.
I can't believe this is anything but intentional. In fact, he did it
a few years ago, and even more blatantly, and halfway from front to
back, instead of the back corner.
Do I have a reason to complain to the guy?

Your neighbor is probably just trying to solve his own drainage issues.
While he may be reckless in the way he handled it, maybe you could just
mention the problem and offer to help find a solution.

"Howdy neighbor, I see you just added a drainline for your downspouts. I
bet that really helps keep things dry over there. Unfortunately, the way
you have the pipes routed, it's flooding the area around my shed. Can I
help you install a drywell to disperse the flow? That way you can keep
things dry over there without flooding my property. Or maybe we can reroute
the lines so it runs off the other direction away from my buildings."

If he's a halfway decent person, I would think he would be happy to work
with you to find a solution that works for both of you. For example, I have
drainlines routed to the back of my property, and if I found out they were
causing issues for my neighbors, I would be happy to fix things so it
doesn't impact them.

On the off chance he's just a jerk, I would just look at it as natural
drainage. He's not CREATING water afterall, he's just redirecting the
natural flows. So how would you handle the situation if it were naturally
occurring? Maybe you could create a swale along your property, or add your
own drain lines to reroute the excess water to areas it won't hurt
anything.

Taking legal matters would be my absolute last resort. It would be
expensive, stressful, time consuming, and create even more tension with
your neighbor. In my opinion, it would just make a bad situation even
worse. He may fix this problem to appease the law, and then find something
else to annoy you with in the future.

Just my two cents,

Anthony