Today, Vine has finally made their six-second videos embeddable across the web. They've also updated their iOS app to allow for embedding (as well as the ability to share other people's Vines on Facebook and Twitter).
"When we launched Vine, we described posts as 'little windows into the people, settings, ideas and objects that make up your life.' With today's update, you can display them almost anywhere," says Vine.
When you reach the embed screen, you can choose your size as well as two modes - simple mode and postcard mode.
Simple embeds simply show the Vine, with the pertinent information like user, description, hashtags, etc. shown when you hover.
Postcard mode shows all of that info in a white frame around the Vine video:
In order to embed a Vine via the iOS app, tap on the "..." button within any Vine video. Click "share this post" and then finally "embed." you'll get an email with the code, which will take you to the embed page. Make your size and mode selections and there you go. Copy the code and put it up on your site. It's not exactly without its annoyances, but it's about as easy as embedding on through an app could be.
You can embed your own Vines, or anyone else's Vine as long as they've already shared it on Facebook or Twitter.