There are both many parellels and much contrast in today's intenational dangers and the Cold War. Although the Cold War seemed to threaten total annihilation, in many respects today's situation is worse.
1. Pakistan. If a militant terrorist organization succeeded in seizing Pakistan and it's nuclear weaponry this could be a serious problem. This isn't as frightening perhaps as the USSR and US killing everyone on earth in a few hours, but it would be bad. A nuclear-armed al-Q'uida is an idea the rest of the world wouldn't like. It could lead to severe sanctions, even land invasion by UN forces or strikes by almost anyone with a large enough air force. It would not drive a wedge between the Cold War protagonists, though; the Western Allies, China and the former-Soviet countries would probably all cooperate.
2. The Balkans. A perrenial trouble spot, and there will probably be another war there within the next few years as Kossovo continues its independant course from Serbia. Kossovo is the ancient sacred heart of Serbia, but is now populated mostly by Albanians. During the Cold War the ethnic troubles in what was Yugoslavia were kept under control by Tito, but no more. This is a conflict that has the possibility of the US and Russia taking opposite sides. Sort of like Vietnam, but more center-stage.
3. International terrorism. This is the most complex threat in every way. Such groups have advantages in timing, seeking soft targets and controlling the level of intensity, but are susceptible to military action, police forces, investigations of all types, infiltration, observation by vigilant citizens, etc. In addition, terrorists are usually considered criminals, not soldiers, and are therefore not covered by the Geneva Convention if captured. Even if they were considered soldiers, as non-members of recognized national armies they would be treated as mercenaries, again not covered by the Geneva Conventions. In some ways this situation is reminiscent of the Cold War in that there are two diametrically opposed forces, but the forces are radically different. The disparity of force means the war must be fought as a series of intelligence and guerrilla engagements, with one side preying largely on the defenceless and the other retaliating in ways which ensure collateral damage too often.
4. Mexico. One-party rule, inattention to the problems of the poor and the long-term foolishness of politicians in Mexico have combined with the failure of the American "War on Drugs" policy to create chaos in Mexico which is spilling over into the US. The bankruptcy of American policy has enabled drug syndicates to grow more in terms of firepower and aggression than in business acumen, and Mexico has done nothing about the basic economic inequities in the country. Illegal and legal immigration has spread Mexican drug gangs across the US, and Mexico itself is approaching civil war. This is somewhat like the Cuban revolution, but far more dangerous. This is economic and social conditions approached by criminal gangs instead of an ideological revolt.
5. Israel. Same as always, things haven't changed much here. The US will still back Israel, although not unquestioningly anymore. The US also must keep cooperation going with Arab countries because of al-Q'uida, etc. The USSR still largely supports Arab countries. As for the last 6,000 years, war could come here at any time.