All I know of is xLib, but I'm sure there are others, so what are they and which ones are the best/most used/still frequently updated?

Well to list all of them would be a large task indeed, but there are only a few worth mentioning in my Opinion:

xLib APP: But you already knew this
XCOPY PROGRAM: Can copy archived programs to RAM and delete them.  Very very usefull and very very small
CelticII PROGRAM: Usefull for manipulating appvar/program data.  Can (un)archive both and access/write data.  ABout 2000 bytes if i remember correctly
Omnicalc APP: Has basic sprite routines, but differs mostly in its advanced linking routines.
CelticIII APP: Has all of xLib's features implemented the same way (with the same syntax) but not only is faster, but also has all the capabilities of CelticII and a lot more.  The elite of Basic Libs.

My personal favorites are CelticIII and XCOPY for Basic games.  CelticIII because it allows me to play xLib games as well (for which there are a surprising number ) and has a LOT more features!  XCOPY because it gives a lot more memory to BASIC games while being incredibly small itself.

EDIT: Ninja'd

There is also Omnicalc, which is more limited in game commands, but has sound commands and inline assembly support (like Axe). Unlike Asm( command, inline asm is much faster. Omnicalc has some issues on the new OS, though.

Finally, for those who prefer smaller libs, even if it means it will waste several bytes of RAM, there is a program version of Celtic called Celtic II, there is CODEX, which does a lot of stuff xLIB does, but much slower (see ROL3 for an example of how slow), Xcopy, which does the same thing as real(10 in xLIB, Resource, a more complex but larger version of Xcopy, Zcopy, another one, slightly smaller, but it only runs on OS 1.12 through 1.14, Flash Gordon, which is similar, but works a bit differently and was pretty much obsoleted by Xcopy, Zapi, which does some funky stuff such as scrolling parts of the screen and some CODEX stuff and finally BASIC Tools, which does some of the CODEX stuff plus more, but each programs are separate so it can save memory if you don't need all small routines. Another nice lib is Zpic, which allows you to recall pics from archive including the hacked pics that can be created with ZSTO or Devpic8x, and I heard of Xtravar, which apparently grants access to all normally innaccessible but possible pic, string and other variables.

There is also two program versions of xLIB. Both has tilemaps and sprite supports but are much more limited and slower. I keep them in case people might not want to have a massive 16 KB APP

Btw, it is possible to have grayscale like in Pyoro using xLIB, Celtic III or Omnicalc (the later being slower, though, as seen in Reuben Quest series). There are a bunch of tutorials avaliable for this in the downloads section as well as a tool by Nitacku. I don't recommend grayscale unless you are pretty good at BASIC and alerady made large games before, though.

Yeah true, it's like enabling the Français or Español application, giving access to special characters in the CATALOG. You use ASM to access these chars but your game still remains pure BASIC, as it can still run without any pure ASM program

ZTrumpet, I think the extra lists are useful, because they're only 2 bytes, where as any list you make is at least two bytes.   BTW, how would you use those hacked Pics and GDB, since the basic commands use numbers?

You can use tokens as arguments to the Store and Recall commands. Try it with Pic1

I've always wondered if there is overlap between xLib's extra PICS and XTRAVAR's Pics... I'm guessing that they do.

Some others:
FlashGordon, though it sounds remarkably similar to XCOPY
VARASM, which checks if a variable exists/archived
GBA, for platform games, but it's in French
TLib, random things that you really ought to use CODEX for, and it's in Spanish

XTRAVAR, xLib, and Celtic III all give you access to all of the 256 Pic vars, and they are the same.  So yes, xLib pics are the same as XTRAVAR if you have the same Pic number.
(It's worth noting that xLib and Celtic II are required when the program is run, but XTRAVAR is not.  This is why XTRAVAR is "pure" basic. )

I think I'll add this to download section soon, it migth be easier to find in the future.