The beauty of formal manners is that their strict rules give shy people a framework in which to interact, and they ensure that every attendee has plenty of opportunity to meet a variety of people.
In 19th-century Britain, wealthy and well-born families were brilliant at getting singles together. You can use their rules at modern dinner parties and dances. Seat singles randomly, boy-girl-boy-girl, at a singles dinner party. During appetizers, they must chat primarily with the person on one side; then, during dinner, with the person on the other side. Keep similar formal rules with dancing. Give each woman a dance card listing the order of songs to be played, and require that she never dance more than twice with the same man, that she should spend that block of time with a man on her dance card, or that each single of either sex should dance every dance. Rules for dancers should not be enforced in any way. Their simple existence will encourage mingling.
At Christmas or Valentine's Day, a gift-giving singles event can bring people together quickly.
Require all attendees to purchase a gift that reflects themselves but that they think others would like as well, and bring it wrapped appropriately to the event. Have each single draw a number from a hat. The person with the number "1" chooses the first gift and unwraps it. The next person has the choice of taking the first gift or choosing another wrapped gift from the pile. Once all gifts are distributed, have gift givers tell recipients who they are and why they chose that gift. Encourage mingling by bringing hors d'oeuvres and drinks around.
There is nothing like a masked ball for bringing shy people together.
Participants can simply wear masks or wear costumes as well. You can follow the rules in the first section above, or have no rules at all. At a costume ball, have participants commit to talking and behaving (within reason) like the character they have adopted, if possible. Masked balls are a good singles event for Mardi Gras season or Halloween. They can also add interest to a warm summer night if you use Shakespeare's "A Midsummer Night's Dream" as the theme.
Bring Your Pet
If many of the singles you are working with have pets, a "bring your pet" event in the park can also bring couples together.
Use Disney's "Lady and the Tramp" or "101 Dalmatians" as the event's theme. The venue should include a wide-open area for dog walking as well as a comfortable indoor area for cats and other pets. Arrange seating groups both outdoors and indoors that encourage intimacy and conversation, and have groomers, veterinarians and others on hand to give formal or informal lectures and demonstrations. The biggest problem you'll have in an event such as this is pets who cannot be well-behaved in a group. If you anticipate this, start with very small groups of about 10 to see how things go.
Children can also bring people together, but they are more likely to keep singles far, far apart.
Rent out an entire Chuck E. Cheese or Gatti Land for an evening and have an informal get-together for singles with kids. You can let the event be free-form, or have child-style games for adult participants only, such as Twister or three-legged races.
Add an element of learning to your singles events.
You can bring veterinarians and groomers to a pets event. Don't stop there. Bring singles together for a cooking experience with a gourmet chef. Try hiking excursions to learn about local plants and geology. Gardening, horseback riding and boating classes will attract singles with shared interests. The key is to have a roughly equal male-to-female ratio, so choose topics that will attract both sexes equally.