The minimum-fuel (Hohmann transfer) travel time to Mars is about 8 months each way. It's possible to shave some off that time by using more fuel, but fuel-to-payload ratio is among the biggest engineering factors in ambitious space missions.
However, the alignment of the planets has to be just right to get that fuel-efficient course, and after reaching Mars the spacecraft would have to wait another year or so before heading home -- or spend vastly more fuel to make the trip. That makes the whole mission take about 32 months*.
Currently, our long-term space station missions have involved regular resupply from the ground; a round-trip Mars mission needs to go more than two and a half years on its own. That's a lot of supply cargo you have to carry and a lot of things that can break along the way, which means carrying a lot of weight in spare parts and/or people to maintain the equipment.
Mars's 1/3 g is about twice that of the moon, so you can imagine that a landing craft would need to pack a lot more engine and a lot more fuel than a lunar lander. Each ton of payload on a rocket incurs many tons of engine and fuel on the lower stages -- looking back to the moon missions, it's something like 75 tons of Saturn V paying for 1 ton of Apollo spacecraft.
Our moon landers only stayed on the surface for a couple of days. We'll be staying at Mars for more than a year, so we'll send a bunch of unmanned cargo flights in advance to drop off supplies and building materials for the surface station. That's more launches, but the payload and reliability requirements for those are relatively modest.
We could send unmanned fuel tankers to rendezvous with the mission in Mars orbit; the total fuel requirement for the mission wouldn't change, but the primary spacecraft could be a little smaller this way, at the cost of a more complex (i.e. failure-prone) mission profile. Another option is ISRU, refining fuel on Mars itself for the return trip, but that's another fairly risky proposition, probably only suitable for the lander's ascent back to Mars orbit, if that.
The atmosphere of Mars is awkward; unlike Earth, it's not dense enough to give the lander free braking (once a returning spacecraft reaches Earth atmosphere, it doesn't need to use any more fuel to land safely, just drag and parachutes), but it is just dense enough that the landing craft has to be built with aerodynamic considerations (again a huge contrast to the lumpy Apollo LM). Which means, yep, more weight.
None of these problems are themselves insurmountable, but building and flying such a thing would be many times larger and more complex task than the Apollo flights. No nation presently has the will and budget surplus to make that happen.
*) If you can provide another 5km/s of ∆v -- requiring a launcher about 5 times as big -- you can cut the total mission duration in half, with a 30-day stay on Mars instead of a 336-day stay.