We don't get
Goldeneye- a generation of kids don't argue about watching each other's side of the screen, and TTL's
@Meadow goes through life with an odd listlessness.
In general, a lot of 90s technothrillers are going to have to find something else for their villains to do without all those Soviet surplus superweapons floating about following the lax security standards the transition to capitalism brought about - hey, that's what happened per these works.
In general though I suppose it does depend on what form the continuing Cold War takes as it goes into the 90s and the 20th century. Pop culture was often reflexive when referencing the Cold War, whether directly or metaphorically, to whatever the feeling was at the time. Look at the evolution of nuclear disaster as portrayed in popular films - in the 50s it was metaphorical through giant bugs, then in the 60s it was very direct with all those flashpoints, as a genre it decreased in number during the 70s at the time of détente, before coming back bigger (and more realistic) than ever in the 80s as a result of increasing tensions. That's something of a simplification, and as with everything there are exceptions, but it does show how things would change depending on what's going on politically/militarily.
It's difficult to speculate without a skeleton of an idea for how things progress, but a few things we might know:
James Bond will be very different, it might still go on hiatus following
Licence to Kill since that was as much to do with legal issues as changing political times. It's not going away for ever so long as Cubby is alive, of course, but when it comes back the films may be (plot-wise) closer to those of the 1980s. I'd bet Pierce Brosnan still becomes Bond however, they were gunning for him since the 80s, after all.
That whole slew of films dealing with ex-Cold Warriors at every level now left with nothing to do won't be a thing. This wasn't confined to spy films like
Ronin, however;
Falling Down is steeped in this too with the main character being a defence (D-FENS) engineer laid off.
Strangely enough, we sort of have a weird example of how a major part of 1990s pop culture would have looked if the Cold War was still a thing. In the first season of
The Simpsons the family take in an Albanian exchange student who turns out to be a spy; perhaps we'd have had more instances of Homer saying things like "The machinery of capitalism is oiled with the blood of the workers."