New machines probably won't have a problem. The easiest way to check is to call your computer dealer. Computer manufacturers are also making the information available and offering free fixes. Incidentally, if you own a Macintosh, relax. Even the original Mac was engineered to handle dates up to 2040.
More advanced users can test their own machines.
But I prefer a nifty free program from NSTL that tests the machine more safely and thoroughly. Again, Macs are fine. Finally, take a good look at your other software, especially any custom programs you've written as well as spreadsheet, database, and personal finance programs such as Quicken. Newer versions, especially Version 6 and Quicken 98, can. And with all these programs, remember to type in all four digits of the year.