There are a few things you want to be careful of in buying a DVD player from Europe.
I'm not sure what country you're buying it from, but I live in Germany and have a DVD player.
First, you have to be careful of the format that they use. American televisions use NTSC and European use PAL. This is a compatability between the TV and the DVD player. As far as I know, this is the frame rate at which it plays. Also, my DVD player has an 'odd' connection that it uses that is a 'interconnection' cable between devices called SCART. You may need some sort of SCART adapter to go to American television. To give an example, my VCR is connected to my DVD player by a SCART cable, then another SCART cable connects my DVD player to my television. As far as I've ever seen, American TVs don't have this, but I think they sell adapters for RCA output. So check your connections that come with this DVD to make sure it'll hook up and that it'll play NTSC.
Next, of course, you need to worry about what power the DVD player takes. Does it run off 220 volts? Houses in Europe are only wired for 220 volt and have a different shaped plug.
Last, to answer your question, if you search on the internet for DVD player hacks you will find websites with lists of DVD players and hacks that can be done to make the DVD player play all regions. DVDs are coded by region. USA is region 1, Europe 2, Asia I think is a different region as well. I have done this with my player so I can play DVDs I get from the states as well as DVDs I rent from the store. Just do a Google for DVD player hacks. Of course, I take no responsibility to any damage or problems you have doing this.
Good luck. Hope that helps.