Personally, I generally don't care for crossovers much. To me, it seems like people use it as a substitute for genuine creativity. Not to say that it can't be carried off creatively (Gerard Andrew's
Out of Range, a crossover between NIMH, the Rescue Rangers and the Rescuers, comes to mind as an example of that, though there are a number of other NIMH fanfics that I like much better), but it still requires effort to do it; perhaps even more so, since you have to reconcile the differences between two different sets of settings, characters and plots. For anyone who needs a reminder to what happens when crossovers go bad, I refer you to the infamously bad
Rangers of NIMH[=http://linkchecker.stacken.kth.se/mst3k/]Rangers of NIMH crossovers (link goes to MiSTed version, as it is the only way to experience this 'classic' piece of... work).
That said, crossovers can be fun; especially when they don't take themselves seriously. I've thought it might be cute to see a NIMH and
Dangermouse[=http://www.clubdm.com/]Dangermouse crossover.
I can't help but comment on your suggestions--just so you know, I'm not criticizing you or your ideas, this is just what I think when I think of a crossover between NIMH and your suggestions. Maybe someone could carry them off well.
1. Star Trek - Yeah, I know what image you're talking about; I always thought it was
one of the funnier images[=http://www.thornvalley.com/gallery/fan/singshow/nimhtrk1]one of the funnier images Ken Singshow did. That said... Eh... I don't think it'd work so well. The Secret of NIMH has a strong 'fantasy' base that'd be hard to work into the colder 'sci-fi' base of Star Trek. Again, might be eligible for a 'fun' crossover, but not something I'd ever take seriously. I'd personally rather see a fanfic about the Rats of NIMH far into the future--perhaps they've attained the technology to do spaceflight of their own? Maybe they've 'integrated' somewhat with human society? Maybe humans have destroyed themselves, and they, being hardier creatures, have survived to pick up the pieces that are left? Now that I think about it, I can't believe what a great, unexploited well of ideas that is.
2. Watership Down - I've only seen the movie once, so I don't remember it that well. I suppose it could work, but you'd have to figure out a way to get rabbits and mice to interact in a way that makes sense. lishrugsli
3. The Lord of the Rings. If you're plannng on anything to be taken seriously, then no. Absolutely not. About the only thing I can think of here would be a slightly humorous retelling of the story with mice and rats instead of Hobbits and Men. And even then, that sounds like a bit of a stretch.
4. Who framed Roger Rabbit? - Short answer: Uh... No. Slightly longer answer: Only if you do it more from the 'Roger Rabbit' side, and again, would have to be a 'fun' type crossover. Otherwise, no.
5. Babe - The feel of NIMH and the feel of Babe are so entirely different in my mind that I can't even envision a possible crossover that'd work well. Might as well try to do a crossover with Charlotte's Web.
Anyway, that's my $0.02.