For months , Uzbekistan's erstwhile allies in the Collective Security Treaty Organization have been discussing in public what they intend to do in regard to Tashkent's suspension of its membership in the group. When the CSTO finally held its summit meeting last week  in Moscow, the group did the only thing it really could: accept the inevitable and try to put the best face on it. Russian Foreign Minister Sergei Lavrov visited Tashkent just before the CSTO meeting, saying  "It is Uzbekistan's sovereign choice [to leave the CSTO]. We regret it, but the decision has been made... However, Uzbekistan, remains our ally, our strategic partner."
The CSTO did suggest that Uzbekistan can't just float in and out of the group, as it did once before, reported  Russian newspaper Vedemosti:
“"Regrettably, it did certain damage to the image of the organization," admitted Russian Representative to the CIS CSTO Igor Lyakin-Frolov. "All I can say is that the door back remains open. Membership is Tashkent's for the asking." President of Belarus Alexander Lukashenko meanwhile said that certain terms of the renewed membership had to be met... if it ever came to that. "Uzbekistan will have to ratify all our decisions and agreements first," said Lukashenko. When Tashkent returned to the CIS CSTO in 2006 after the suspension in 1999, it never bothered to ratify guideline documents of the organization..
What the significance of this is depends on your interpretation of the CSTO's real goal, and why Russia has put so much effort in recent years into building it up. It's not yet clear whether the organization is a serious effort to deal with insecurity in Central Asia, or merely an attempt by Russia to strengthen its influence over its former republics in Central Asia. In the latter case, it's only a loss for Russia's sense of itself as a regional power; in the former, it could weaken collective efforts to deal with an unstable Afghanistan after the U.S. starts pulling out in 2014.
It will be easier to reach decisions in the CSTO, now that Uzbekistan isn't there to gum up the works. For one, plans to develop CSTO joint military armed forces could get easier, something that also was discussed in Moscow:
CSTO presidents opted to strengthen the military component of the organization. "The CIS CSTO is a military alliance, after all," said Lyakin-Frolov. "It is only logical for it to be thinking of the military component... considering the complicated situation in the world in general and the fact that three member states are located in Central Asia."
But those decisions will have less weight, given how central Uzbekistan is to Central Asian security. Analyst M K Bhadrakumar, a former Indian ambassador to Uzbekistan, says  the move shows Uzbekistan's successful multivector diplomacy, getting what it wants out of big powers like the U.S., Russia, and China, without giving up its sovereignty in return.
Tashkent’s recent legislation banning all foreign military bases on Uzbek soil and affirming its determination to steer clear of all military alliance systems would testify to the country’s robustly independent foreign policy. Equally, the single-minded propensity to view any paradigm in regional or international politics through the prism of self-interests is a consistent feature of Uzbek diplomacy. Added to these would be the country’s high sense of destiny as a regional power and a pivotal state in Central Asia with a burning ambition to keep all options on the table to realize its objectives in its ‘near abroad’.
The International Crisis Group's Deirdre Tynan, though, tells uznews.net  that Uzbekistan will come crawling back into Russia's arms once the short-term alliance with the U.S. runs its course.
One element that is unfortunately missing from all this analysis is the internal political factor. Karimov is likely now more focused on domestic issues (stability, succession, etc.) and his foreign policy moves are likely subordinate to those. Unfortunately, the internal political dynamics in Uzbekistan are very opaque, so it's hard to say what might be behind this decision, and whether he might reverse it again in the future.