Then there is Contra. Below is a quote from this.

"What is contradancing?

Contradancing is in many ways like "old-time square dancing done in lines." The dances are designed so that you and your partner will dance with every other couple in these lines. The caller will teach each dance, telling you everything you need to know (no classes are necessary). The dances are done with a smooth walking step, and no fancy footwork is required. We always dance to live (and lively!) music provided by a range of talented dance musicians. Reels, jigs, waltzes and related tunes from American, Canadian and British Isles traditions predominate, and the fiddle is often a featured instrument.

You can find much more detailed descriptions of contradancing at Gary Shapiro's Contradance page and at Rich Futyma's What is a contradance? page
. There's also a marvelous description of contradancing by Greg Rohde here.

We're an exceptionally friendly group, with people of all kinds, and an age range of 7 to 70 (more or less). Our events are both smoke and alcohol free. Dress is casual, although we request that you bring non-scuffing shoes to help protect the wood floor (tennis shoes are fine). You don't need to bring a partner. Even if you do, we encourage you to dance with other people also - you'll both learn more quickly that way! If you're new to this, we'd also suggest coming at the beginning of the dance, since that's usually when the caller teaches most carefully, with newcomers in mind."

It's a lot of fun, and has evolved from the longways dances of Jane Austin's day to some high energy twirling, flirting and swinging at "Zesty Contra" clubs.