What is the importance today of John F. Kennedy's Inaugural Address?

The importance of the speech depends on one's perspective. On the one hand, it was an extremely bellicose speech, and was heard that way at the time. The speech was given at a time when Cold War tensions were extremely high, and Kennedy was speaking directly to the Soviets when he said that

we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe to assure the survival and...

The importance of the speech depends on one's perspective. On the one hand, it was an extremely bellicose speech, and was heard that way at the time. The speech was given at a time when Cold War tensions were extremely high, and Kennedy was speaking directly to the Soviets when he said that

we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe to assure the survival and success of liberty.

Kennedy always saw the Cold War as his first priority, and the speech reflects this emphasis--he was speaking, he said, at "the hour of maximum danger" to freedom. But he also extended what might be interpreted as somewhat of an olive branch, observing that both the United States and the Soviet Union were "overburdened by the cost" of nuclear weapons and asserting that neither side should be afraid to negotiate. So this speech is a fairly good summation of Kennedy's priorities upon becoming President, and is this important as a document of the Cold War. But we also remember this speech for its soaring rhetoric, especially his injunction to Americans near the end of the speech to "ask not what your country can do for you--ask what you can do for your country." Thus this speech is a sort of statement of the civic ideal that many Americans still hold. So for these reasons, both historical and rhetorical, this speech retains great significance.