Do you want to build relationships with interesting people?
Here are some unique ways to meet new people, get out of your comfort zone, and have great conversations:
There was a CEO that I really wanted to meet, but I was never able to connect with him at social events. So I wrote him an email with the subject line: "Can I buy you lunch?" In the email I said: "You're a business leader that I really respect. I want to get better at x. Can I take you for lunch?" He replied and said: "I'd love to go for lunch, but you don't have to buy."
Everyone likes being taken to lunch. Be generous, and you could receive enjoyable company, and great advice, in return.
This one isn't for everyone, but I've been able to have amazing conversations with interesting people through the podcast I run with Kyle Fox: Product People. Podcasts are great, because you can choose a topic that you're passionate about, and then invite other people (that are passionate about the same thing) to join you as a guest.
You don't need to be naturally outgoing or extroverted to podcast. Some of the best hosts I know are actually the opposite! Here's a good resource for getting started.
Kevin and Jared didn't like the other networking events in town, so they decided to start their own: Nerds Night Out. Instead of doing the "normal" thing, and have a presenter, they just get together for drinks at a pub. They started small by inviting a few other people in the web development community. They told them they'd do it every month. It gradually grew, and now 10-25 people come each month.
One way to meet a completely new group of people is to take a class in a different city. I took a weekend "learn to code" class in Las Vegas. It was actually easier meeting people as the "out-of-towner" because I was unique (I was the only non-local). I still keep in touch with people from this class.
Every event organizer needs help: a photographer, a sound person, a host (to welcome people). When you volunteer, you get to meet the organizing team, and anyone attending the event (plus, you usually get to attend and participate for free).
I built the website for a fundraiser. Peter volunteered to do the video for a workshop I was running. Here's a tip if you're a photographer: why not volunteer to take photos of attendees throughout the night? As you take photos, offer to email people their photographs. You've made a meaningful connection, and you have a great way to follow-up.
I hope these techniques are helpful! If you're feeling nervous, this article might help.
What are techniques you've used to meet new people? Reply in the comments with your stories. Have questions? You can ask me on Twitter.