I bought a burgundy colored mandevilla vine this year and it is beautiful. Different than the usual pink or white. Sorry but don't know what the variety is.

Akebia!

Do you mean foliage or flower? If flower, then clematis could work. I've posted a likely suspect below. :)

Here is a link that might be useful: Clematis Niobe

Not sure if you mean the vine or the leaves or both, but there is a little known vine, a BEAUTIFUL burgundy vine with dark green leaves that has little blooms that look like tiny bunches of varigated pink to burgundy grapes. It's Malibar Spinach (red vine variety). It's delicious in salads or just to pick off the vine and munch. It has a nutty flavor and it will twine itself around your heart! It is not supposed to come back every year but mine re-seeds and does anyway. Google it. It grows to about 10 feet tall. I think if you ever had one, you'd never want to be without it.

If you want some red Malabar spinach vines I have plenty. They have to be trained and tied to grow upright because they don't have tendrils to anchor to anything. It grows naturally as a sprawling vine on the ground. I've trained some of mine along a deck railing and it really is a beautiful plant. Mine get much larger then 10'. The stems and foliage are striking and the berries are a beautiful deep purple, almost black. It doesn't get a flower, just the berries. I personally can't stand the texture but the taste is fine. It's mucilaginous, kind of like okra. It's a perennial in warm climates. Another beautiful vine with deep purplish red tubular blooms is the asarina but I'm not sure how large this gets. I'm growing it for the first time this year. In the frost free zones it will grow year round, otherwise it's grown as an annual. I believe it comes in a variety of colors, mine just happens to be a wine color. I'd have to check the tag to see what variety it is.
Karyn

I second the akebia, mine bloom a wonderful purplish red and smell like chocolate Mmmm.

Rangoon creeper opens pink and turns burgundy. Wonderful exotic fragrance. Please see link below. Grow well in Florida.

Here is a link that might be useful:

My Rangoon Creeper opens white and turns red. I'd love to find a burgundy one.
Karyn

Definitely Clematis and there are so many to choose from.

Versailles, Bourbon to add a few more names.

wanda