I don't have a Linux box at home, so I'd like to use my Raspberry Pi to try out some development on Linux. Will binaries compiled on it run on other, more standard Linux boxes, or will they only run on the Raspberry Pi?
No, the binaries will run only on similar ARM-powered Linux boxes, not an X86 PC (for example.)
Not really for fully featured dev work, unless you really do love command line based IDEs and editors rather than graphical ones. Simple messing around with text editors / compilation will be fine though.
The major problem is the speed of the interface. At present, with X not having GPU acceleration, even relatively simple applications such as the web browser run pretty slowly for me. Fully featured graphical IDEs would be unusable, even if they did run (which I'm unsure about due to memory requirements.) Some of these issues may be mitigated when X gets GPU acceleration.
Speed of compilation can also be an issue for some languages such as C++, though is less of an issue with others (C / Java.)
To all practical intents and purposes, the stuff you compile on the Pi will only run on the Pi (well technically other ARMv6 platforms.) You technically could cross compile, but I'd argue whether that's really worth it!
In short, if you want to play around with a bit of development work with standard editors then it will do, but you'll probably find yourself getting frustrated quite quickly if you move onto anything more serious.