>>1
I'd prefer the Sepples approach: You should be able to implement anything in the standard library yourself if you felt so inclined. If there's one thing Sepples did right, it was the roughly equal support (improved to pretty much equal in Sepplesox) for user-defined stuff and intrinsic library stuff.
That way, if a certain implementation rubs you the wrong way, you can just as easily create your own roll - the language should support both just as well. To me, that's more important than having a ton of offerings for the standard library.
As far as things I'd expect to be in a standard library for a general-purpose language, I'd expect things used in almost every project: Easy utilities for strings, time zones, various data structures such as stack and queue (though this is by no means an exhaustive list of structures), various sorting utilities, Internet-related tasks (synchronous connection and data handling, at the very least), threading facilities. Things like that.