Windows comes with a tray clock and, yes, it displays the time. However, many think that it is too basic in its functionality and would wish for more features and display options. There are a few free tray clock replacements out there that might just do the extra bit you're looking for. Here is a review of the ones I favor.
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TClock Lite is a vastly improved replacement for the standard Windows tray clock. It provides all the benefits of the original as well as many enhancements and a number of useful additional features. It achieves this with a tiny footprint and doesn't even require installation. Given the tiny size, the power of this program is most impressive. Less impressive is the help file which is brief and not particularly helpful. However, the program is so well laid-out and simple to use that it's not really an issue. You might get a warning from your security software that TClock is potential spyware. It's not. It's just picking up the fact that it modifies explorer.exe to display the clock. The 2nd link below is to the Japanese author's site. You'll see some strange characters displayed but the "download" (sic) link is clear enough.
If you want an alternative, try the classic TClockEx that offers similar functionality to TClock Lite. It hasn't been updated for a while, but appears to run OK on Windows XP systems.
LClock is my last, but by no means least, recommendation. It pops up its own calendar with a single click on the tray clock, which you can use it for reminders and to-dos. It all works marvelously well and you get a clock display that looks like the one in Vista. LClock is based on TClock lite but doesn't allow a simultaneous time and date display.
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