I think a lot of it depends on what you want to get out of the trip. We took our son for the first time when he was 18mos, and I don't regret it for a moment. We have absolutely priceless video of him running over to get his picture taken with Mickey, hugging the Pooh characters in the evening on the verge of exhaustion, and interacting with performer-after-performer in the old Tapestry of Dreams parade at Epcot.
To us, 15+ mos seemed to be about the right time. We at least wanted him walking, and when I say "walking" I mean really getting around well on his own. We also didn't want to deal with bottle feedings while on vacation.
In fact, our daughter will be about 18 mos when we take her for the first time this December.
Others have taken children when they were months or even weeks old. Infants can enjoy any WDW attraction that doesn't have a height restriction. They can join you on everything from It's A Small World to Pirates of the Caribbean to the Haunted Mansion.
Obviously there are a number of developmental milestones that may impact your decision. If you'd rather your twins be speaking in sentences, you may want to wait until age 3. If you want them to be able to ride some of the more adult rides, you might have to wait until age 4 or so. Our son will be nearly 4 this December but is already 42" tall in bare feet. He can't wait to ride Star Tours and Test Track, both of which have a 40" height requirement.
If you don't want to pay for the twins, go before they turn 3. Children under 3 get free admission to the theme parks and they even eat free at buffets.
The only consideration that I would recommend completely sidestepping is the "we want him/her to remember it" topic. I was 7, nearly 8 yrs old on my first trip to WDW. Even at that age I have exactly three memories of the entire day--buying a mug at a gift shop, another member of our party chickening-out as we boarded Space Mountain, and listening to "If You Had Wings" over and over again because the ride didn't require a ticket.
Now those are some magical memories, eh?
Go when you're ready to go. Take a ton of photos and video. Even if the kiddies don't explicitly remember the trip, they'll watch the home videos for years to come.