It is possible to create a view, though it's a bit complicated:
wget --post-data='name=ViewX&mode=hudson.model.ListView&json=

' http://.../jenkins/createView

Both parameters "name" and "mode" are required twice, as POST parameter and in the json argument. If one is missing, Jenkins responds with "400 Bad Request".
I think this URL is not meant to be used as remote REST API, but it actually can.

I would suggest to fix the problem above, so that either POST parameters can be used or a JSON snippet can be posted.

another option:

java -jar jenkins-cli.jar -s <jenkins_url> groovy createView.groovy --username <user> --password <passwd>

where createView.groovy contains

hudson.model.Hudson.instance.addView(new hudson.model.ListView("ViewX"))

Found this by looking through the source code:
It is possible in Jenkins 1.509.4 to create views via the REST api

view.xml:

 
<?xml version="1.0" encoding="UTF-8"?>
<hudson.model.ListView>
<name>MyView</name>
<filterExecutors>false</filterExecutors>
<filterQueue>false</filterQueue>
<properties class="hudson.model.View$PropertyList"/>
<jobNames>
<comparator class="hudson.util.CaseInsensitiveComparator"/>
</jobNames>
<jobFilters/>
<columns>
<hudson.views.StatusColumn/>
<hudson.views.WeatherColumn/>
<hudson.views.JobColumn/>
<hudson.views.LastSuccessColumn/>
<hudson.views.LastFailureColumn/>
<hudson.views.LastDurationColumn/>
<hudson.views.BuildButtonColumn/>
</columns>
</hudson.model.ListView>

Create the view:

curl -vvv -X POST -d @view.xml -H "Content-Type: text/xml" http://localhost:8080/jenkins/createView?name=MyView

Get the configuration:

curl http://localhost:8080/jenkins/view/MyView/config.xml

Update the view:

curl -X POST -d @view.xml -H "Content-Type: text/xml" http://localhost:8080/jenkins/view/MyView/config.xml

@Patrik
Should we consider the issue as "Resolved"?

Oleg: Needs to be documented on the /view/Foo/api page, similar to 'Create Job' on /api.

this solution works pretty well with few limitation:

• nestedView plugin does not register it's own class and curl end with exception that NestedView is not resolved.
• in case of subviews, xml needs to be extended with <parent> node, unfortunately in case of coping view a to b, parent node is not visible.