Random events are interesting; they add stochasticity which simulates reality, but - as one poster mentioned - everyday reality isn't very random.  What may seem random has more to do with the fact that we couldn't predict that it was coming.  So.. when I walk out of my house and get hit by a baseball thrown by some particularly clumsy neighbourhood kids, that might seem random, but it actually had a cause.  I just didn't know about the cause until my eye socket was swallowing a baseball.  Now when I get to work and have to give a presentation with a black eye maybe my ability to impress my co-workers is diminished, and nobody would really blame me because how could anybody be ready for that?  But again, it wasn't actually random.

As such, I would love to see a game (ANY game) that introduced stochasticity where I can't predict the event occurring, but it actually had a reason for happening, and perhaps that reason can be understood if I would invest the time into figuring it out.  Borrowing from the topic example, if my chief engineer tells me one morning that his staff are feeling particularly spry today and my ship's efficiency is enhanced, maybe that's because morale improved when I opened up that peculiar crate of mushrooms on Planet 9 from Outer Space.  The subsequent loss of 15% of my crewmen may also be an effect.

Now, that's not random in that if I play the game again and open that crate of mushrooms again the effect will be the same (or at least similar), but it is similar to random in that I can't predict the consequences of my actions at the time that I take them.  The timing of an action could well have a different effect, of course, and open up layers of events that could greatly increase replay value.  The Metal Gear Solid series has demonstrated some exciting layering in this fashion.

In opposition, you could have completely random effects conferred by the crate of mushrooms, in which this time I play I get effect X, and next time I get effect Y.  If I like effect X and not Y, I might save-scum until I get effect X, which is not (in my opinion) a desirable gameplay consequence.  Of course, the random event is probably a lot easier to inject from a game design standpoint.

Just some mushrooms for thought..

Edit: Upon reflection, I suppose the mushroom crate's effects could be randomized at the start of the game, thereby circumventing save-scumming and making the curiosity of opening the crate quite exciting with each playthrough.. although I guess if I didn't like the results I could just restore my game and not open the crate......  Ah, save scumming.  I hate myself for using it, but I can't stop myself!  If only my willpower could be randomly enhanced!

I'm in favor of random events - but not necessarily of the "engineering breakthrough" variety. Instead rather "space" random events that affect everybody equally (barring racial special abilities). For example a form of ion storm that crops up in space - affects navigation and weapon systems; but it does so for everybody in the storm.

Other random events can be of the form of random encounters - where a random encounter is not the same as a combat encounter.

How about this random event:

1. You're flying through space.

2. Radar blinks and there's another ship flying through.

3. You decide to engage and it turns out to be a lone Kzer-Za dreadnought.

4. First thing you notice when in battle is that your enemy isn't engaging and isn't fleeing. Also, his ship is beat up and looks like it's about to explode.

5. You decide to withdraw your weapons and just come closer.

6. Enemy ship does the same thing.

7. When you're close enough - you open your docking bay and capture the enemy vessel.

8. It turns out to be a lone Kzer-Za deserter that doesn't agree with Eternal Doctrine. His comm system was shot, so he couldn't radio you.

9a. You get his ship repaired and put in your satellite fleet. The deserter turns out to be an excellent pilot, so your flagship gets its turning rate increased by 5%.

9b. You get a suicider on your ship and he blows couple of your satellite ships up in hangar. (doesn't really make sense, but passable as an example)

9c. You get an enemy spy that gets caught, converted and sent back to spy for you. Your map about enemy territory gets more detailed. From time to time you get informed about POI in enemy territory.

If you chose not to engage - random event is over.

If you chose to engage and kill him - random event is over.

If you chose to engage, but just left the combat - delayed event triggers later in game: The deserter, impressed by your combat honor, arrived to your starbase with Dreadnought schematics (now you can build it).