Champions is a complex system for sure - and as a GM you almost certainly need to know more than your players. However walking through character generation with novices allows you to keep control of the power levels.
A simpler system was
Marvel Superheroes but I have no idea how easy that is to get hold of. But once I'd got my head around Champions, I didn't look back. (Never tried V&V)
Other non-superheroic options: (caveat - most of this would have to be sourced 2nd hand as I have no clue how "in-print" these games are now)
For Sci-fi, West End Games'
Star Wars was very simple to learn and play. It's a good action orientated system that doesn't get bogged down with rules. There's also not much need to flesh out the gameworld as pretty much everyone has seen the films. You only come unstuck if you're around players that know more than you about the timeline you've chosen. I have no idea what WoTC have done with it but it's probably bad.
Star Frontiers (the TSR version) was also a relatively simple system (thought quite old) and is very playable once you have Zebulon's Guide.
Then there's
Paranoia (West End Games version) which is immensely slapstick in its approach and a lot of fun. Our last game of it was entitled "how many troubleshooters does it take to change a lightbulb?" by the end of which we'd decided it was "more than 6". In WEG fashion - the rules are very simple.
Torg (West End Games) was an excellent game set in a (sort of) apocalyptic Earth and very "heroic". Interesting rule system and sometimes difficult to GM for, but stories would often write themselves.
Lastly, my favourite Sci-fi would be
Shadowrun. I never bought anything past the FASA years, so can't comment on the quality of the game under the various new owners, but it was rich in gameworld flavour and extremely easy to generate entertainment of an evening with nothing prepared beforehand. The rules can get complex, and I needed to change a few here & there, but it was fun while it lasted.
Contemporary games... Well I only ever ran 2. First up -
Call of Cthulhu. From the 1st Edition box through to the 5th edition hardback, not much has changed with the rules. There is very little to learn but it probably requires the most work as a GM (or keeper in Chaosium speak). However there are some amazing campaign books released for it. Masks of Nyarlathotep took my gaming group just over 1 year (1/week for 3-4 hours) to complete. Characters die in this game. Various supplements have been released over the years including contemporary sourcebooks (Delta Green) as well as a terrible idea of converting it to the D20 system.
The other game I ran was
Danger International. Not even a wikipedia entry for this one, but it basically uses cut down Hero System (Champions) rules and can easily be emulated with a copy of the Hero System rulebook.
Most fantasy games are complicated. There's the D&D monster of course, but I really loved
Middle Earth Roleplaying which was comparatively simple. MERP uses a cut down version of Iron Crown's
Rolemaster RPG which is complexity incarnate. But boy - you've got to love those critical tables. A whole book of them!
That's my tuppence!
-H