Should MySpace be shut down?

That kind of activity can take place anywhere, including here. Solicitation for sex on the internet is nothing new, nor is trolling the boards for potential victims for all sorts of crimes. I think they could help deter it a bit by not allowing so much personal information to be posted in the profiles, but you really can't stop someone altogether from giving out whatever information they want to.
In my opinion, no, they shouldn't shut it down. The site is more than just predators and perverts.

TSA has it right. Shutting it down would just send the kids elsewhere. If anyone using MySpace has problems, it is up to their parents or guardians to solve the problems.

Myspace could, I suppose, try to be more careful in policing its members, but otherwise their chief obligation is to cooperate with law enforcement whenever asked to. But a few nasty bits of bathwater should not be an occasion to discard the babies.

I'm sure in 1806 that some girls got pregnant while walking home with an escort--invited or uninvited--after choir practice.

The problem isn't that MySpace exists. The problem is that any number of kids haven't been taught protective boundaries between their public and private lives.

Some kids have been seduced through MySpace. Other adolescents have been nabbed as underaged drinkers and drinken drivers because they have posted their dubious exploits--with pictures.

Exactly. Myspace is the medium; the problem is what these kids are posting and/or who they're pursuing offline as a results of postings. But predation has been around as long as, well, as long as Zeus was seducing shepherds (both male and female, if I recall correctly). What these kids are doing is more a function of their own poor judgment and/or their parents not keeping up with what the kids are doing. While I appreciate the minefields that must be parenting and the teen years these days, well, Myspace isn't responsible for these shenanigans any more than the US Postal service is responsible if someone becomes penpal to a convict and then decides to let that person come to their house.

Should the internet be shut down? Phone lines cut? Parks closed? Public areas turned into private prisons?

Predators are everywhere.