Should the usage of DI/IoC remove all occurrences of the “new” keyword?

Question

Should the usage of Dependency Injection and an Inversion of Control container remove all occurrences of the "new" keyword from your code?

In other words, should every object/dependency, no matter how simple or short-lived, be "registered" within your IoC container and injected into the method/class that needs to use them?

If no, where do you draw the line between which dependencies/objects get registered in the IoC container, versus what gets created "in-line" as a concrete reference, via the new keyword ?