Any maneuver that one needs to perform on a space mission requires a certain change in velocity, called ΔV ("delta vee"). To complete a mission you need to add up all the ΔV to produce a ΔV budget. For instance, the ΔV budget for Apollo looked something like this (rough numbers):
Ascent to LEO = 9000 m/s
Tranlunar injection = 3200 m/s
Lunar orbit insertion = 900 m/s
Lunar descent = 2100 m/s
Lunar ascent = 1900 m/s
Transearth injection = 1000 m/s
There's not a lot that technology can do to change the ΔV budget, so it's just a matter of how the ΔV can be produced. There's really only two ways that I can see to do this: (1) use more efficient staging, or (2) use more efficient propellants/engines. As far as staging goes, Apollo was pretty efficient - this was the purpose of adopting the lunar orbit rendezvous method. There might be some ways to squeeze a little more efficiency out of it, but I suspect those improvements would be small. That leaves us with propellants/engines.
The Saturn V was pretty efficient as far as propellant went - it used LOX/RP-1 in the first stage and LOX/LH2 in the upper stages. It is, however, possible to use more efficient engines. Both the F-1 and J-2 where open cycle engines and, therefore, had lower specific impulse than is possible with closed cycle engines (i.e. staged combustion). Although closed cycle is more efficient, it is also more complicated and expensive. There was at one time talk of adapting the space shuttle main engines (LOX/LH2 staged combustion) for use in future heavy launch vehicles, but I'm not certain of the current status of that. I think the plan was dropped because of the cost, instead favoring an upgraded version of the J-2. Staged combustion has never been used on anything approaching the size of the F-1, so we'd be getting into uncharted territory. Future heavy launchers are likely to make extensive use of SRBs, which are powerful and relatively cheap, but have lower specific impulse than LOX/RP-1.
The Apollo spacecraft itself used hypergolic propellants, which aren't especially efficient in terms of specific impulse. Back when the Constellation project was being considered, the plan was to use LOX/LH2 in the lunar lander. The Orion service module would use hypergols just as Apollo did, though LOX/methane was considered at one time. The staging was also going to be modified. The lander's descent stage would be used to perform lunar orbit insertion rather than the service module. The only major maneuver that the service module would perform was transearth injection. I don't remember if the lander was to use LOX/LH2 in both the descent and ascent stages or just the descent stage. Regardless, this meant that somewhere between 3 km/s and 5 km/s ΔV would be switched from low-efficiency hypergols to high-efficiency LOX/LH2. This would certainly lower the amount of propellant needed to produce the required ΔV.
I don't know exactly how the 400:1 ratio was derived (see below), but there are certainly some things that can be done with propellants and engines to be more fuel-efficient than Apollo. However, with current technology, I think the improvements would be marginally small.
(ETA 1)
The entire Apollo-Saturn vehicle contained about 2700 metric tons of propellant, thus 1/400th of that is 6.75 t. The total mass recovered at splashdown was no more than 5.5 t, which is closer to a 500:1 ratio. More importantly, the entire 5.5 t did not "land on the moon". The only portion of that to have actually been on the lunar surface was two astronauts, the lunar samples, and some other odds and ends. Probably not more than about 300 kg made its way from the lunar surface back to Earth, which is more like a 9000:1 ratio.
(ETA 2)
OK, I just read the quote from Virtual LM and is says that "the fuel-to-payload ratio was 400 to 1, meaning that for every pound of payload required for the trip to and from the Moon it would require some 400 pounds of fuel to get the job done." The quote doesn't specifically mention landing on the moon and is non-specific at to exactly what payload is. If we're talking about something like an Apollo 8 mission, then 400:1 sounds about right.
