This is interesting in all kinds of ways.
First, the initial move to Amazon was a clever one. In the old days, a concerted and continuing DDOS attack on a small site might have seen them off - nowadays there are plenty of commercial reasonably priced or free cloud hosts. So cloud computing can be seen as a bulwark for freedom of speech - vive les nuages!
Second, though of course, what strokes your back can also bite it, and here we have Amazon suddenly coming over shy. This appears to be entirely the sensible legal thing for them to do and anyone accusing them of bad behaviour should be accused right back of utter naivete. Amazon are now on notice from the government of hosting material which breached US national security and so would according to the US Espionage Act as quoted in the Guardian piece, fairly clearly have been at risk of guilt as a person who "knowingly receives and transmits protected national security information" if they had not taken down. (Though see a contrary view here.)
While Assange as an Australian not a US citizen, and a journalist (of sorts) might have had defences against the charges quoted also ( as canvassed in the Grauniad piece) Amazon, interestingly, would, it seems, not. They are American and by definition for other useful purposes (eg CDA s 230 (c) - see below and ye ancient Prodigy case) , not the sort of publisher who gets First Amendment protections. And Amazon has its CEO and its major assets in the US, also unlike Assange. I think that makes take down for Amazon a no-brainer. (And also interestingly, CDA s 230(c) which normally gives hosts complete immunity in matters of liability which might affect press freedom (such as defamation by parties hosted) does not apply to federal criminal liability.)
But as Simon B also pointed out, there are lots of other cloud suppliers , lots in Europe even. What if Wikileaks packs and moves again? Would any non US`host be committing a crime? That would depend on the local laws: but certainly it would be hard to see if the US Espionage Act could apply, or at any rate what effective sanctions could be taken against them if a US court ruled a foreign host service was guilty of a US crime.
Which leaves anyone wanting to stop access to Wikileaks, as Technollama already canvassed, the options of, basically, blocking and (illegal)DDOS (seperating the existence of the Wikileaks site from any action against Assange as an individual). Let's concentrate, as lawyers, on the former.
Could or would the UK block Wikileaks if the US`asked?
Well there is an infrastructure in place for exactly such. It is the IWF blacklist of URLs which almost all UK ISPs are instructed to block, without need for court order or warrant - and which is encrypted as it goes out, so no one in public (or in Parliament?) would need to know. This is one of the reasons I get so worked up about the current IWF when people are asking me if I won't think of the children.
There is also the possibility, as we saw just last week, of pressure being exerted not on ISPs but on the people who run domain name servers and the registrars that keep domain names valid. Andres G suggests that the US might exert pressure on ICANN to take down wikileaks.org for example. Wikileaks doesn't need a UK domain name to make itself known to the world, but interestingly only last week we also saw a suggestion from SOCA (not very well reported) that they should have powers effectively to force Nominet, the UK registry, to close down UK domain names being used for criminal purposes. Note though if you follow the link that that power could only be used if the doman was breaking a UK criminal law.
But there is a really simply non controversial way to allow UK courts the power to block Wikileaks. Or there may be soon.
Section 18 of the Digital Economy Act 2010 - remember that? - allows for regulations to be made for "the granting by a court of a blocking injunction in respect of a location on the internet which the court is satisfied has been, is being or is likely to be used for or in connection with an activity that infringes copyright."
Section 18, at present, needs a review and regulations to be made before it can come into force. This may in the new political climate perhaps never happen - who knows. But what if that had been seen to?
Wikileaks documents are almost all copyright of someone , like the US government, and are being used ie copied (bien sur) without permission. Hence almost certainly, a s18 fully realised could be used to block the Wikileaks site.Of course there is some possibility from the case of Ashcroft v Telegraph Group  EWCA Civ 1142`that a public interest/freedom of expression defense to copyright infringement might be plead - but this is far less developed than it is in libel and even there it is not something people much want to rely on.
So there you go : copyright, the answer to everything, even Julian Assange :-)
Oh and PS - oddly enough the US legislature is currently considering a bill, COICA, which would also allow them to block the domain name of sites accused of encouraging copyright infringement. Handy, eh? (Though on this one point, the UK DEA s 18 is even less restrictive than COICA, which requires the site to be blocked to be "offering goods and services" in violation of copyright law - which is not even to a lawyer a description that sounds very much like Wikileaks.)
EDIT: Commenters have pointed out that official government documents in the US, unlike in the UK do not attract copyright. Howver the principle stands firm: embarrassing UK docs leaked by Wikileaks certainly would be prone to attack on copyright grounds, including DEA s 18, and it is quite possible some of the current Wikileaks documents could quote extensively from material copyright to individuals (and Wikileaks prior to the current batch of cables almost certainly contain copyright material).
Interestingly Amazon did in fact, subsequent to this piece, claim they removed Wikileaks from their service, not because of US pressure, but on grounds of breach of terms of service : see the Guardian 3 December 2010
"for example, our terms of service state that 'you represent and warrant that you own or otherwise control all of the rights to the content… that use of the content you supply does not violate this policy and will not cause injury to any person or entity.' It's clear that WikiLeaks doesn't own or otherwise control all the rights to this classified content. Further, it is not credible that the extraordinary volume of 250,000 classified documents that WikiLeaks is publishing could have been carefully redacted in such a way as to ensure that they weren't putting innocent people in jeopardy. Human rights organisations have in fact written to WikiLeaks asking them to exercise caution and not release the names or identities of human rights defenders who might be persecuted by their governments."
The copyright defense is alive and well :-)