Like tmgeorgo says, you can use PVC and the appropriate adhesive. The adhesive, generally purple, actually chemically melts the plastic together. I think it would be strong enough for a wine bottle, but i'm not sure. Obviously you're not using the stuff according to its design. If you go that route, make your design similar to the one above- a good base and rather vertical.

I wouldn't trust any solutions for metal pipe that didn't involve welding.

If you're going to use plastic pipes, then the solvent used for sealing joints is probably good enough.  It dries fast, so practice some before you start.

 For metal pipes, maybe some gorilla or elmers ultimate glue?  Seems like an easy DIY, just glue things on one at a time and use books to prop things up and keep them from sliding around as you glue on the pieces at different angles.

This is a great idea, and probably a SUPER easy DIY project: PVC Pipe cut to size, whatever spray paint fits your decor, and...  hmm, some industrial adhesive or maybe even small screws?

I especially like the idea of putting different diameters together: perfect for the smaller "sampler" bottles of wine, and the great big fat ones that don't fit anywhere else.