In a broad geopolitical sense, Turkmenistan is a buffer zone of sorts. It lacks the resources and access for significant global influence. Instead, it occupies the southern end of the former Soviet Union, nestled next to everyone's good friends Iran and Afghanistan. I recommend a couple long, but generally very good reads from Stratfor. The first is from a couple years ago on The Geopolitics of Russia which is available without e-mail registration through the magic of Google cache. The second is part of that same series from earlier this year on The Geopolitics of the United States, Part 2 which can also be found through Google cache here. The relevant portion (for today) is the section near the end on Russia and how it can be a threat to United States' interests.
In the eyes of some Russians, the portions of Central Asia that used to be part of the Soviet Union (Turkmenistan, Kazakhstan, Uzbekistan, Tajikistan, Kyrgyzstan) are like wayward children. Sure, they may not be under direct control of the Kremlin, they're still here for the taking. This is a condition that these -Stans generally dislike which is why various attempts are made to escape the influence of Moscow. What I wrote about several weeks ago on the diminsihing availability of Russian language teaching is an example of the desire to separate from Russian influence.
For the United States, Turkmenistan along with the rest of Central Asia is a good buffer against Russian influence further south. The United States already uses Turkmenistan air space for flights on the way to Afghanistan. American regional interest is pretty clear: War on Terror (whatever that means) and some level of strength projection. Like the Cold War when the U.S. had military bases in many places along the Soviet perimeter, the U.S. currently maintains bases in the region at Manas, Kyrgyzstan and Karshi, Uzbekistan.
Turkmenistan, like its Central Asian brethren, ends up in the middle of continuing struggle for influence in the region. Day-to-day lives go on and Turkmenistan has an opportunity to have a great deal of say in how it progresses from here. However, it is ultimately boxed in by the geopolitical reality surrounding its position. The struggle has often in the past been between the United States and Russia, but there are now China and India to also accommodate.