Here's a small collection of big iron. First a couple of "Doctor Who" stories: there is an Elliott 405 in "Day of the Daleks" and an ICT 1301 in "The Monster of Peladon". Then there are a couple of appearances of the GE 635 that I missed the first time round in "Spaceballs" and "Get Smart, Again!".
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Here are some appearances of 1950s and 1960s computers. The short-lived series "Turn-On" had a crucial role for an IBM 1620. The "Agents of S.H.I.E.L.D." episode "Alien Commies from the Future!" has panels from the ever-popular IBM AN/FSQ-7. Finally, the "Doctor Who" episode "Meglos" has some old British machines: the ICT 1301 and, making its Starring-the-Computer debut, the Elliott 405.
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Starring the Computer