If your twins are a bit older, perhaps they'd enjoy dressing as Drake and Josh or, if your twins are girls, one could dress as Miley Cyrus and the other as Hannah Montana. Some other great twin costume ideas are salt and pepper shakers, a right shoe and a left shoe, a cracker and a slice of cheese, or a round pasta noodle and a meatball.
It can be great fun dressing infants up as politicians or other famous people. Since they're infants, they won't care, but you can almost guarantee others will get a kick out of them. Perhaps one twin can go as John McCain and the other Sarah Palin - if you're a Republican, that is. Or, you may choose to dress the kids as celebrities, such as Brad Pitt and Angelina Jolie, Tom and Katy, Bill and Hillary or even Oprah and Stedman.
Even dressing up at opposites can be great fun, such as Obama and McCain, or even something as simple as a cat and dog. One twin could be a police officer while the other is a prisoner, dressed in striped shirt and pants, perhaps with a plastic ball and chain around their ankle. Having the kids dress as a mouse and a mousetrap or even as you and your spouse can be very cute, too.
Often, twins want similar costumes. If that's the case with your twins, there are still plenty of options that will allow them to be somewhat the same, but still quite different. Dressing the twins as superheroes, such as Batman and Spiderman, is similar yet will give the twins a different look. So will the Dora and Diego idea mentioned earlier. Perhaps each child wants to dress as their favorite Crayon - similar but each will be a different color, or they both want to dress as an M & M of their favorite color.
Also consider a bumble bee with a pot of honey, or Winnie the Pooh with a pot of honey; Thing 1 and Thing 2 from the Cat in the Hat; ketchup and mustard; salt and pepper (mentioned above); and Mickey and Minnie. Perhaps the twins are old enough to enjoy WebKinz. If so, let them dress as their favorite WebKinz.
Since you know your twins best, you will know right away if they would want to dress similar or as complete opposites. Once you've determined that, you've got these ideas to get you going!