I've planted the Lonicera periclymenum species, which is very much native to the UK. I'm also looking to plant the other type, Lonicera xylosteum, in the coming months. If you're in the US though I believe it could well be an invasive species from Europe.
Yes, I'm in the US - Minnesota in fact. Our worst bush/tree invader is Buckthorn, but Honeysuckle is right behind it. I believe both were introduced as garden plants.