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Apollo 11 used the Saturn V rocket, which is no longer produced. As far as I can tell, Atlas V rockets are not as powerful and would not be able to deliver the lunar lander to the surface of the Moon.
If we were to launch another Apollo mission to land on the Moon today, do we have a rocket powerful enough to do it?
From the questions wording you mean, could we lift the Apollo CM/LM stack on any existing boosters? In that case no. Largest heavy lift vehicle is probably Delta-4-Heavy. Falcon Heavy is not yet operational and will exceed it, but has a low Isp upper stage so is not optimal for such missions.
Could a different moon mission be launched? Almost certainly, just a matter of launching in smaller pieces and likely refueling in orbit. Would it be worth it? Well clearly no one has thought it worthwhile to date.
You would launch something like the Command Module and Service module (In one or two modules), where the Service module would act as an upper stage, and then refuel it in orbit from following launches. Then another launch for a Lunar Module, assemble in orbit and onwards.
There is a lot of speculation that the Falcon Heavy demo payload might be an Apollo 8 style mission, where a capsule is sent to go around the moon and come back.
If there was a true desire to do so, it is likely possible, but no one has decided it is necessary.
Additionally, consider costs. A Saturn V in modern dollars has been estimated in \$2 billion dollar range a launch. A Delta 4 Heavy is around \$400 million a launch. A Falcon Heavy launch is advertised at \$125 million. (Assuming they ever develop cross feed). Thus even 5 Delta 4 Heavy launches is competitive with a Saturn V, and as many as 16 Falcon Heavy launches.
With the experience of building the ISS a lot of technology and tools for in space assembly has become much more feasible than in the 1960s on a tight deadline.
We probably no longer need a giant super booster just for the moon, even though SpaceX plans to build one as the BFR/MCT combo for Mars missions.
No. But two ideas about how to do it aren't far off, although I doubt it will be done that way.
Falcon Heavy, which would be three Falcon 9 first stages put together and which will test fly in September 2016 (if not postponed again and again). It would require two launches. One that lands an empty ascent and return vehicle on the Moon, and a second which lands an astronaut or two next to it.
Russian Angara 5, which would be the heaviest launcher in the world today and has been successfully test launched in 2014, but in a yet uncomplete configuration, has officially been proposed to send kosmonauts to the Moon with four launches that assemble the lunar mission in low Earth orbit.
I remember reading in Bill Bryson's - a short history of nearly everything that we no longer possess a rocket powerful enough to send a man to the moon! Apparently the historic Apollo 11 plans were destroyed sometime in 90's by NASA during a spring clean.
