and more importantly
Bonus points:
Lua has been developed for this very purpose. Scripting languages like Ruby and Python have excellent C/C++ bindings and there exist good, yet experimental (beta) bindings for .NET and Java in the form of JRuby/Jython and IronRuby/IronPython.
Whatever you do, please, please, please use one of these languages. Don't make the mistake of creating your own application-specific scripting language, and don't use any of the obsolete alternatives (Tcl, Guile, VBScript, etc.).
I have had a really good experience with Angelscript, the documentation is pretty good and the author and community are very helpful. I have also used Lua and Python, but I found that Angelscript felt the most natural to me.
Both of the were designed to be embedded in other programs. Personally, I prefer Tcl as I find it a lot more readable and, well, it's it's one of the most dynamic languages out available.
Angelscript is to much C like. If you're planning to share your script with programmers only it's great. But we used it once in a 3D engine, and we had a problem people, who were not exactly coders, comparing it's too comlicated.
I would recommend Python. It's really easy to embed in any language that has decent C interoperability and there are a number of tutorials on it. It only took me a couple of hours to figure out how to embed it having no prior experience.
Also, if you're working in C++ then Boost.Python makes exposing your existing classes/functions a snap.
The one place it probably loses out to some of the others is the memory requirements.
Previous tips like Lua (very preferrable) and Python / Ruby are excellent. If your software however is written in Java, there are quite some other possibilities, like:
Of course, there are also Python and Ruby implementations in Java.
My personal choice would be Python, but I recommend that you have a look at SWIG, if you are using C/C++. You can then use it to generate the wrappers for a variety of languages including Python, Ruby and Lua. It makes adding the bindings much easier.
We have used SWIG to create python bindings for our application.
V8 JavaScript Engine is worth mentioning - supported by Google, and you are embedding a language that is easily more popular than the other suggestions. See JavaScript: The Lingua Franca of the Web.
Lua is not only designed specifically for this, it's very small in codesize and memory footprint, and it's the fastest non-JIT language available. And, of course, it has one of the very few full-blown JITs available for fully dynamic languages (only x86 for now).
It's written in ANSI C, and is already working in several small microcontrollers. There's a well-supported patch for non-FPU CPUs. The included libraries are all optional, so you can just not include what's not useful for your device.
here is a good summary of how Lua can help on small devices.
Don't forget about PowerShell... PowerShell can be embedded in any .NET application as a scripting language.
I recommend Lua.
Lua is written in ANSI C which is the lowest common denominator for languages. Lua can be integrated into an embedded C program by linking the libraries. Utilities exist to call Lua functions from C code, and C functions from Lua code. Lua has a very small footprint, making it great for embedded systems and video games.
A friend of mine integrated Lua 5.0 into a high-performance DSP application on a TI digital signal processor. There was no operating system, and a few libraries. The DSP code was written in C or assembler. He managed to port Lua to this platform. He found that using Lua on this platform approximately doubled his productivity because the edit-compile-link-load-initialize-test cycle was reduced from about 20 minutes to about 1 minute for simple changes. When he showed a demo to the customer, and the customer wasn't quite satisfied with some aspect of the code, he quickly changed the code while it was running (by transferring Lua scripts to the processor) and it then behaved properly. (The customer was impressed). The only issues they had was the occasional failure of the garbage collector, but that problem was fixed in Lua 5.1. In spite of using Lua, overall the real-time critical DSP application worked fine.
Asides from that application, Lua is known for being the valuable scripting language embedded in platforms such as World of Warcraft and many other games and game engines.
I put up a video on YouTube that shows how to use Lua with the SQLite database.
I've seen Python inside quite a few software packages, and it seems to be working just fine (I'll mention just Tecplot 360 cause it's currently open in the other window, but there are a lot others).