Web browsers already try to isolate tabs from each other. Chrome pioneered the principle of "one process per tab" and other browsers followed. This kind of isolation was meant for reliability more than security: when one tab crashes, e.g. because of a bug in a plugin, prevent the whole browser process from dying as well.
Using VM techniques, be they Unix-level jails or even full-blown hypervisors, can help in the case of a tab being subverted: through some security hole, an attacker manages to run his own malicious code in your browser. The VM will then try to contain that attack. Note that the problem has far-reaching consequences: for instance, a Web browser must be able to read local files, in order to support Web sites which ask for upload of a local file. When complete isolation is enforced, functionality is decreased.
If you want complete isolation, see Qubes OS: this is a Linux-based operating system which launches small VM for individual applications (or group of applications) and would allow you to run several browser instances which cannot see each other.
The problem, though, is that you usually don't want complete isolation, and hostile full-process hijacking is rare. Browsers already apply some sort of isolation which does not use hypervisors, but is (usually) effective. Security issues don't come from the breaking out of a tab process, but from the communication channels which are maintained between tabs by the browser in order to implement required functionality. The Same-Origin Policy is an important concept which is part of the issue: the SOP incarnates the security model which the browser enforces, and most security issues with Web browsers are due to the fuzziness with which the SOP boundaries are defined.
To make an analogy, consider a brick wall with a door in it. Using hypervisor technology would be akin to reinforcing the wall and the door frame with steel. This is not bad, but won't help very much if the real problem is that the door is not locked. When trying to enforce isolation between browsing instances, the really hard thing is to define precisely what may be shared and what should not; hypervisors operate at a lower level and are just tools to enforce a policy, but the policy must first be defined.