The NeXTSTEP "Workspace" and file manger were replaced with Finder in OS X. Finder was a direct port of the classic Mac OS Finder, implemented in C/C++ using the gnarly but powerful Carbon file manager APIs rather than Objective-C, Cocoa, and the comparatively limited NSFileManager APIs (limited icon support, no file alias support, no asynchronous or interactive file operations, etc.)
The Carbon Hot Key APIs came from Classic Mac OS and are still the only way to do global hot keys in OS X. They're one of the few bits of Carbon still supported in 64-bit OS X.
I also miss the NeXTSTEP menus, as for a big display, they are much easier than scrolling up to the top of the screen.
NeXTMail evolved into Apple Mail. Preview and Terminal retained their functions and their names. Digital Librarian (indexing specified files) was succeeded years later by Spotlight. Unfortunately we lost Digital Webster, a nice thing to have before the days of always-on Internet connections, which I think was linked to all apps via the command-equal-sign. Interface Builder survived. WebObjects survived. There was a TextEdit-precursor, but the very nice lightweight word processor WriteNow from a third party did not survive to be included in OS X.
The OS X Finder is recognizably similar to later versions, maybe >2.0?, of NeXT's Workspace Manager, with the primary navigation the same (albeit with the scroll bar on the bottom instead of the top and favorites on the top instead of the left). The original NeXT design was probably cleaner. And I still miss a dock that you can flick up and down.
I have a NeXT cube in my home office closet. I've turned it on in the last few years and it works, but the original 660MB hard drive -- a monstrosity for its time! -- has failed. :(
It got ported to Java, back when Apple still wasn't sure to keep Objective-C or port everything to Java.
Nowadays I think it is in life support.