Is Continuous Integration important for a solo developer?
The benefit of CI lies in the ability to discover early when a check in has broken the build. You can also run your suite of automated tests against the build, as well as run any kind of tools to give you metrics and such.
Obviously, this is very valuable when you have a team of commiters, not all of whom are diligent to check for breaking changes. As a solo developer, it is not quite as valuable. Presumably, you run your unit tests, and even maybe integration tests. However, I have seen a number of occasions where the developer forgets to checkin a file out of a set.
The CI build can also be thought of as your "release" build. The environment should be stable, and unaffected by whatever development gizmo you just add to your machine. It should allow you to always reproduce a build. This can be valuable if you add a new dependency to your project, and forget to setup the release build environment to take that into account.
The basic concept of CI is that you have a system that builds the code and runs automated tests everytime someone makes a commit to the version control system. These tests would include unit and functional tests, or even behavior driven tests.
The benefit is that you know - immediately - when someone has broken the build.
This means either:
A. They committed code that prevents compilation, which would screw any one up
B. They committed code that broke some tests, which either means they introduced a bug that needs to be fixed, or the tests need to be updated to reflect the change in the code.
If you are a solo developer, CI isn't quite as useful if you are in a good habit of running your tests before a commit, which is what you should be doing. That being said, you could develop a bad habit of letting the CI do your tests for you.
As a solo programmer, it mainly comes down to discipline. Using CI is a useful skill to have, but you want to avoid developing any bad habits that wouldn't translate to a team environment.
As other people have noted, CI does have advantages for a solo developer. But the question you have to ask yourself is; is it worth the overhead? If you're like me, it will probably take an hour or two to set up a CI system for a project, just because I'll have to allocate a server, set up all the networking, and install the software. Remember that the CI system will only be saving you a few seconds at a time. For a solo developer, these times aren't likely to add up to more than the time it took to do the CI setup.
However, if you've never set up a CI system before, I recommend doing it just for the sake of learning how to do it. It doesn't take so long that it isn't worth the learning experience.