Due to its immense size, the Museum of Science and Industry handles crowds as well as any indoor museum in the Chicago area. The main problem points are getting in, getting lunch, and any small one-at-a-time experiences, like "driving" the tractor in Farm Tech.
Crowds are worst during school breaks, especially when it's cold out since the zoos won't pull as many away. Chicago Public Schools winter and spring breaks will be the busiest, although any week near spring break is likely to bring lots of out-of-town visitors. The summer break is busy, but not nearly as packed. Illinois free days will also be more crowded (check for upcoming dates on MSI's site)
Order your tickets online ahead of time, since the ticket lines get very long when the museum is busy (plus, if you're adding any additional exhibits/movies, you'll be able to book the times you want before they sell out). See the tickets page for more information. If you want to visit free exhibits that require tickets (like the Idea Factory or Numbers in Nature: tickets are free, but they come with a specific time to spread out crowds), you'll want to get those shortly after you arrive on busy days.
Plan to have lunch around 11 or shortly after on busy days (and really by 11:30 even on less busy days). Even if you're bringing your lunch, the public tables fill up quickly.
Lastly, Idea Factory and Farm Tech tend to feel the crunch from crowds more than most other exhibits. You can still go to both, but kids will need to be more patient to wait in line for the tractor and combine at Farm Tech, or to play with different stations at Idea Factory. The U-505 tour, the transportation gallery (with the model trains) and the 727 handle crowds the best.
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