I was wondering if, using the rockets we have today (I'm guessing the most likely candidate is the Falcon Heavy), we could send at least 1 human to Mars. For arguments sake, let's ignore the fact it would need to be human rated, and assume there are no anomalies during flight. Will the boosters need to be expended as they may need to use all their fuel to allow the crew module to get to the surface? Let's also assume the person(s) aren't returning. Thanks
So according to wikipedia, a Falcon Heavy can carry 16.7 tons to Mars transfer orbit. This is fully expendable (thanks to @JCRM for pointing out this ink), it's much less with full reuse. So we have 16.7 tons into which we need to fit a lot of things:
Consumables to keep the astronaut alive for six months or so: Expedition Mars by Martin Turner gives a figure (p101) of 5-10kg of consumables per day, so that is 1-2 tons for a one-way Mars shot. Could be a little less if your astronaut was a very small woman.
The capsule itself. A reasonable minimum for this might be the mass of the lunar module ascent stage (excluding fuel) which was a very cramped, desperately mass constrained vehicle for two. This is just over 2 tons.
A heat shield and either parachutes or rockets for a Mars landing. As a rough proxy for this, consider an Apollo command module at about 5.5 tons. For one person and just using it for descent we might get away with a bit less. But we probably need bigger parachutes and rockets to soften the touchdown, so lets stick with 6 tons.
So the total of obvious necessities is about 10 tons. This looks pretty possible, we still have 35% margin for the stuff I didn't think of. On the other hand this would be a miserable voyage. Six months on minimal rations cooped up in a tiny space in zero G, followed by re-entry and a tricky landing, from which you basically get to crawl away and die of oxygen deprivation, dehydration or starvation whichever gets to you first, on the Martian surface.