Not in the US, although Boxing Day is celebrated in the UK, Australia, Canada, and several other former British colonies.
Prior to Christmas on the 25th, some people observe
Advent, which starts on the 4th Sunday before Christmas (usually end of November or first part of December). Other people observe
Christmastide, or the
12 Days of Christmas for a period of about 12 days after December 25th.
However, all of these are Christian religious holidays, so observation practices (including dates and lengths) vary by denomination, and aren't celebrated by non-Christians. Some denominations of Christianity may not observe them either, or place little significance to them.
If you wished to take time off to observe them, you'd have to use some kind of personal or vacation leave, since they're not federally observed holidays.
As Mike said, there's no standard practice, but most business shut down all or part of Christmas day. Many companies or organizations do give employees at least a few days off around Christmas and perhaps again for New Year's, but that varies widely.
I work for a college, and we happen to get off Dec. 24th - Jan. 3rd. Again, that's just my particular college, and I'm pretty fortunate to get that lengthy of a paid holiday.