I'll take a quick stab at some parallels:

1. Global in scale and a competition between two ideologies.

2. Like the cold war, there were some hot spots, and victory in the hot spots for the big players (U.S. and the USSR) was so much a physical victory (win a battle), but rather a psychological victory where we both aimed to defeat the support base at home. The communists defeated ours during Vietnam, we defeated theirs during Afghanistan. Neither were important in themselves.

3. Like the cold war several countries that would not normally be important strategically to our national interests like Algeria, Somalia, etc. have become very important (it is like a another Domino Theory), one falls to radical Islam, then another, etc.

4. It is a moral fight on the international front.

5. Political Islam is not communism, but like the Cold War it is an effective ideology at mobilizing populations (or segments of the population) around the world. It is subversive in nature, and initially starts off as terrorism, and gradually evolves into a full scale insurgency (much like a Maoist approach).

6. Like the cold war each side attempts to win more players over to their global coalition. We have the coalition of the willing and they have the Al Qaeda associated movements.

7. Like the cold war a large part of the war will be fought covertly.

Very loose parallels admittedly, and the more I look at the less I like it. I do think are important lessons that we take from the Cold War though (ones most if not all on this site know), and that is the importance of maintaining support of the critical audiences whether they be in our own citizens or in England or in Spain. The damn them, we'll do it on our own approach won't work. Coalitions are critical (why do you think the Al Qaeda makes such as effort to sever them?), and if we have to compromise on some issues to keep the coalition together, then we have to compromise. Realpolitic isn't pretty.