Most packages are either listed as OK or Unknown, which we can assume is good. Programs Recent versions of many GNU software are ready. Commercial programs also have to be ready, and you should consult the web site of your software for their status. Most popular software programs are ready, but you should consult your vendor to be sure. Conclusion Your distribution, if you have a recent one, will most likely work normally.
Packages are in the same situation.
If you have recent versions of your programs and packages, you should be ready. The situation in the Linux world is much better than in the Windows world, where even Windows 98 has Y2K recommended patches. I think we can safely sleep on January 1st. Our computers should be ready and working the next day.