Landing humans on Mars is a completely achievable feat with current technology—if you are okay with the idea of a one-way ticket.
The problem today isn't the launch capabilities or the guidance systems or the navigation. It is the energetic particles from the sun, which can rip apart DNA. Space travelers returning home from a Mars mission would soon die from this radiation poisoning, if they managed to survive the experience at all. A protective shield would simply be too massive to be practical; assuming no technological breakthroughs, the shield would weigh around 400 tons.
It has been noted that a one-way trip would be more sensible. It has even been suggested that we could send senior-citizen volunteers to the Red Planet, where they could spend their final months conducting experiments, laying the groundwork for future permanent settlements and digging their own graves.
A round-trip Mars mission might be achievable, though—not with faster rockets, but with biomedical advances. Drugs that safely combat the effects of radiation poisoning seem to be the only way to make a voyage back home feasible.
I loved reading this entry about the possibility of sending people to Mars to forge the way into our next frontier. I know I can think of a few non-senior citizen people I would like to volunteer for this expedition, how about you :o) To see the full entry, go over to Scientific American.