tv + video + dvd = ?

It's two words, but does home theater work?

Are you talking about a television with an internal VHS & DVD player? Usually pairings of a a television with a VHS or a television with a DVD slot are seen, but there are some with all three. It's usually referred to as a TV/VHS combo or TV/DVD combo, so a machine of all three would be a TV/VHS/DVD combo. They're convenience doesn't come cheap.

http://www.camcor.com/cgi-bin/bcatalog.cgi/id=1042820863

Home Entertainment Center is a good way.

I'd go with "entertainment center," understood in context as being the TV and related stuff that you have at home.

I am just beginning to see the whole set of "TV plus gadgetry" referred to as just the "TV" unless the speaker really intends to refer to just the VCR or just the DVD, for example. (Recall that even the TV itself used to be referred to as a "TV set.")

In Poland we call it 'a home cinema set' (translated literally) and we usually think of it as a set of audio-video equipment. It doesn't have to be combined into one huge hi-tech contraption but every piece of it stands on its own, separately. Do you think this phrase would work in English? Any other suggestions?

Marta, that would likely be rendered in English as something like "home theater system."

Which gives me an idea; perhaps we could refer to "TV plus stuff" as a "TV system."

a few comments:
Clearly you are describing an all-in-one unit with TV and VCR and/or DVD all included in one chassis.
"Home theater" reallly doesn't work. The problem is that "home theater" already has a different definition. A home theater is an expensive system with a video projector or very large screen TV, plus sound system using dolby and 5 to 7 speakers placed all around the room. A home theater is a system designed to recreate the experience of going to a large movie theater in your own living room.
"Entertainment center" doesn't work either. The large piece of furniture that you put the TV, stereo and your discs, tapes, etc. already has that name. (Also refers to to a similar piece of furniture that adorns some living rooms acting as an over-glorified liquor cabinet)
TV/VHS combo (etc,) is probably a good choice, but still a mouthful.
Wouldn't it be nice if there were one term? Let's coin our own! How about TVR or TVD? maybe TVCR? I could go on all day!

In my house, we call it the TVideo, and my mum wants to buy me a TVD player for my Christmas.

I prefer TVideo.