Installing an ARM toolchain is simple now. Don't build one unless you really need to (or you install Yocto).
apt-get install gcc-arm-linux-gnueabiBack when I wrote it, in the gcc 4.3.3 days, I don't even think gcc had a release manager --- we're talking clean, out-of-the-box build failures here.
It's gotten a bit better since then, but getting hold of a gcc cross-compiler is still painfully, pointlessly hard.
For ARM it takes 90 seconds in Debian/Ubuntu. I posted the command right above.
And the larger chipmakers will provide or point you to relevant toolsets or include them with their IDEs. Even the large independent IDE makers wrap their stuff around gcc now.
But there isn't a MIPS toolchain. Or an m68k toolchain. Or a sparc toolchain. Or an alpha toolchain. Or an SH toolchain. There is a Hitachi H8 toolchain, but it's based on 3.4.6. There's an MSP430 toolchain, but you don't want to use it, as it's achingly old and can brick some modern MSP430 devices. etc.
Typically, when working on an embedded device, the very first thing you do is spend far too many frustrating hours trying to beat gcc into shape, and that shouldn't be necessary. The fact that the packages for all these things aren't built and pushed to Debian automatically every time a gcc release is done indicates that something is very wrong somewhere...