How should the United States respond to Russia's annexation of Crimea? That depends on the answer to two related questions: Does the Crimean annexation presage a new era of Russian imperialism in its near-abroad? More broadly, is the international community entering a new era in which great power coercive diplomacy supplants the supposedly rules-based liberal world order that the United States and its allies have painstakingly attempted to build over the last 70 years? If the answer to either is yes -- and, unfortunately, it probably is, with qualifications -- then U.S. policymakers need to do a much deeper rethinking of their national security strategy.

Crimea is uniquely important to Russian geopolitical calculations -- it gives Russia a warm-water port on the Black Sea with year-round access to the Mediterranean and therefore the Atlantic. No other piece of real estate is so crucial for Russia's access to markets and ability to project naval power regionally and globally. That explains why Russian President Vladimir Putin is willing to risk international opprobrium and sanctions to secure permanent Russian ownership of it.
The difficult truth for U.S. policymakers is that Russia's intervention in Ukraine does not represent a sudden shift in Russian behavior so much as the next step in its gradual reassertion of strength. For a decade after the collapse of the Soviet Union, NATO expanded and Russia was on the back foot. Under Putin, Russia has gradually become more assertive on the world stage and more autocratic at home.
For example, Russia opposed the U.S. war in Iraq in 2003; opposed the Rose Revolution in Georgia in 2003, the Orange Revolution in Ukraine at the beginning of 2005, and the Tulip Revolution in Kyrgyzstan in 2005; was probably involved in the cyber-attack on Estonia in 2007; suspended its participation in the Treaty on Conventional Armed Forces in Europe in 2007; invaded Georgia in 2008; opposed NATO's action in Libya in 2011; completed Iran's first nuclear reactor, Bushehr I, in 2011; sold arms to the Syrian government beginning in 2012; effectively stopped U.S. action against Syria for its use of chemical weapons in 2013; and finally annexed Crimea in 2014. In context, the last is not a major shift but only the most extreme example of growing Russian assertiveness in the age of Putin.
That is why Russia may not stop at Crimea: Putin may opt to go for most of eastern Ukraine, giving Russia contiguous territory with Crimea and making it more defensible. The area is populated mostly by Russian speakers who, like the Crimeans, may not object (or resist too strongly) to annexation. Western Ukraine, by contrast, is populated by Ukrainian-speakers who would be more likely to put up a fight, and Russia would stand to gain nothing but the culturally significant city of Kiev. Putin is probably too pragmatic to try to annex all Ukraine just for the sake of cultural symbols.
Beyond Crimea and eastern Ukraine, Russia probably does not see the need to exercise such overt leverage over its neighbors -- it already has the influence it needs. Belarus, for example, is already as subordinate to the Kremlin as the latter could wish. If Putin feels emboldened, he might make a play for formal annexation, but that wouldn't change the reality on the ground: Belarus is already in Russia's orbit.
Russia did previously exercise some coercive diplomacy against Kyrgyzstan. Since 2005 it has pressed the Kyrgyz to shut down U.S. access to the air base in Manas, which the latter uses to ship supplies to U.S. troops in Afghanistan. In 2009, the Kyrgyz, responding to Russian pressure, bargained for a much higher rent from the U.S. for continued access. In 2011 the Kyrgyz announced they would not renew the lease anymore, and the U.S. is winding down operations at Manas this year. 
More generally, the Central Asian republics are so economically intertwined with Russia, mostly through gas pipelines, that Russia doesn't need to invade to wield influence. The Russians have stationed troops in Tajikistan with that government's consent since the end of the Cold War to bolster border security with Afghanistan to prevent the flow of drugs and terrorists northwards into Central Asia and Russia.
In Europe, Russian officials may desire more influence but they are unlikely to go after the Baltics or eastern European states because they are NATO members. While Russia (or its mercenary hackers) was probably behind the 2007 cyber-attack on Estonia, conventional military intervention would trigger NATO's Article 5 mutual defense clause and ignite the worst military crisis in Europe since 1945. Putin, again, is too pragmatic for that.
Crimea, for its part, is on its way to becoming a frozen conflict, akin to South Ossetia, Abkhazia, Transnistria, and Nagorno-Karabakh. These are slivers of territory of disputed status leftover from wars that halted without formal peace treaties decades ago. Their legal ambiguity and isolation from international organizations makes them ideal locations for organized crime and way-stations for drug smuggling and human trafficking into Europe. That means Crimea may end up becoming the Russian mafia's platform for global expansion.
What should the United States do? Some critics have debated whether Russia's action represents a return to the Cold War, and counseled the United States to avoid taking actions that might reignite it. That misses the point, or misunderstands the Cold War. The Cold War was simply a continuation of conventional great power rivalry carried on between the two preeminent powers of the mid-20th Century. The Cold War did not differ greatly from the multipolar world that preceded it except in the number of contestants. Even the sharp ideological disagreement was not unique to the Cold War: Protestant and Catholic coalitions faced off in the 16th and 17th centuries, and the Holy Alliance sought to uphold monarchy against liberalism in the 19th.
Russia's annexation of Crimea illustrates that the end of the Cold War was the end of an ideological contest, but not the end of great power rivalry. Russia has continued to play the game of great power competition, as have China, India, Japan, and others. The United States remains the preeminent power in the world, but the new world of increasingly multipolar great power competition has been gradually emerging for several decades. American policymakers have long been schooled on models of international relations centered on bipolar competition, unipolar hegemony, or liberal internationalist cooperation. The best response to Crimea would be for U.S. officials to learn the rules of this game of multipolar great power rivalry -- new to them, but old to most of the rest of the world -- quickly.