Could a similar Cuban Missile Crisis incident happen today?

Not likely. Not in the context of that particular crisis. The issue was the placing of first strike capable nuclear missiles right inside the US' backyard. This was seen as the same as planting an invasion force on somebody's border. Developments in ICBM technology have made it so that you can effectively launch a nuclear weapon from anywhere and have it land anywhere, at least for the United States and Russia. Modern ICBMs achieve low orbit and therefore are able to travel much farther than conventional atmospheric missiles which usually have a range limited to a relatively small bubble around thier launch site (see estimates of North Korea's theoretical launch ranges on their missile if it ever gets off the ground properly).

With that said, this doesn't preclude the arising of an actual issue similar to this. Where in the 60s the range of first strike capabilities was limited so that proximity of launch assets was considered significant, now technology has shifted so that just development has become the issue. This is because primarily non state actors have become a significant threat whereas before states such as the Soviet Union were considered the main aggressors and as such checks via mutually assured destruction and diplomacy could be used to guage and manage threat levels. In addition with the collapse of the cold war threats are now perceived in a more regional way. While Iran with a nuclear capability could arm a terrorist group and aid them in smuggling a weapon into a Western nation, the other consideration is that the acquisition of nuclear capability presents a destabilization of the regional power bases. With Iran being of an adversarial nature to the west's interests the elevation of that state's ability to dictate regional power dynamics through military threat essentially alters the entire game with regards to managing Middle Eastern stability.

Israel itself is a factor to consider in this. While the US would take a long term view of weighing threat, Israel's long history and close proximity causes their current leadership to advocate extraordinary pre-emptive military action to protect them before the threat is even presented. This is a factor not entirely within the ability of the US and other western powers to control. This could force Western action in preventing Iranian nuclear arms development if only to manage the scope of the erupting violence for the sake of preserving some stability.

The best modern example of a 'Cuban Missile Crisis' would be the current Iran-US standoff regarding so called nuclear arms development. In the same way that positioning missiles in Cuba generated new threat, Iran acquiring nuclear power gives them a new degree of power which would effectively force all interactions against their will by the West to take this into consideration and would effectively make Iran into a regional player, someone who must be handled rather than bullied.

As it is currently Iran's ability to allegedly shut down the Straight of Hormuz could see upwards of 20% of the world's oil distribution disrupted. Given our current economic situation this is in and of itself a huge factor when facing Iran in a military sense. With a nuclear weapon on board it would effectively make any action against Iran a major gamble. Its common assumption that if one state uses nuclear weapons it could lead to many or all other states using theirs. Much like the decent into WW1, progressive reactive political and military encounters beginning with Iran could lead to a new uncontrollable world instability sparking conflict involving far more state actors and their alliances than would be safe to handle.

This is the biggest issue with Iran and the bomb and why its the closest you can really get to a Cuba scenario today.