Here's a list of several options for you to consider. Feel free to suggest your own in the comments as well!
- DisneyQuest. This is the first, and most obvious, suggestion for rain days. If you don't know it, it's next to Cirque du Soleil (another rain choice!) in Downtown Disney. For one admission price, you get unlimited arcade games, plus several other "attractions" that use cutting-edge interactive media. For 1994, that is. You'll find better graphics on those "attractions" in your older xbox, but don't sweat it. There's still a lot of fun in this multistory building.
- Smaller Orlando. A rain day is a perfect time to string together the "quarter-day" attractions in Orlando, such as Ripley's Believe it or not, WonderWorks, Titanic Exhibit, iFly indoor skydiving, Airheads trampolines, or the indoor surfing at Fantasy Surf. You might also like the unique Putting Edge mini golf, with black light.
- Fantasy of Flight. For some folks, this might be a half day experience, but it's a tiny ways afield of WDW. It's got a first-rate museum and walk through simulations, then dozens of (indoor) planes to climb on and around.
- Shop. If your vacation plans include outlet malls, there's a big one, mostly covered from rain, called Orlando Premium Outlets. Or try the covered, more traditional Florida mall.
- Dinner Show. There is no shortage of dinner shows in Orlando: medieval, pirate, horse, or gangster themed choices abound.
- Water parks. This is counter-intuitive, which makes it a fantastic choice. Most people abandon water parks when it rains, so you will find lines and crowds nonexistent. And really - you're already wet! One caveat, and it's a huge one: the parks won't let you stay in the water (and sometimes, not even in the park) if lightning is nearby. Summer storms often bring lightning. If it's quick, no problem. But if it lasts all day, you've got an issue.
- Tough it out in the parks. You could always just plan to get wet and stay in the parks. Some summer rain lasts only 10-30 minutes (but this is not universally true). Umbrellas are better if there is no wind, since ponchos make you sweaty and sticky in the Orlando humidity. Buy a rain cover for your stroller from Babies R Us before you leave on vacation.
If you haven't seen it before, check out the link at the very top of the page for "Other Orlando Attractions". It should give you even more ideas!
Kevin Yee is the author of numerous independent Disney books, including the popular Walt Disney World Earbook series and Walt Disney World Hidden History.