What is the largest movie length on a "standard" VHS tape that will fit in the VCR that is in everyone's home? Also for a one-sided DVD, the kind used for normal viewing in the home?

Standard American VHS tape is T120, which is 2 hours of play time on an American machine at Standard recording speed. This tape will give you 4 hours of play time on "Long Play" and 6 hours of play time on "Extended Play". T160's are also available for standard American VHS players, which give 8 hours of play time on "Extended Play". As you can see, the number after the T refers to number of play minutes on "Standard Play".

American and European playing times, however, are different, due to a higher rate of tape length/minute of recording speed on standard American VHS players. An American T120, when played on a European machine, will give 169 minutes of play time on "Standard Play" as opposed to 120 minutes.

Also, there are tapes available for standard European VHS players that have 240 minutes of play time in "Standard Play" on a standard European machine. This would translate to 12 hours of play time in "Extended Play" mode, though I cannot guarantee that European machines have this mode. This same tape, if played on an American machine in "Standard Play" would only have 173 minutes of play time.

So actually, I believe the correct answer is 12, depending on where the home that "everyone" lives in is located. If you limit to American machines, 8 IS the correct answer.

In the U.S. they make 10-hour VHS tapes that are fairly easy to find, too.

I had a "standard" home vcr almost 20 years ago that could put 16 hours on a tape. 8 hours ON EACH SIDE !

Re DVDs.
A standard single sided disc has a capacity of 4.7 gigabytes. Under normal circumstances this can store 133 minutes on video using the mpeg2 recording/compression format at the bit rate that produces pictures of a quality better than SVHS.
The higher the quality (higher the definition) of the recording, the less the duration will be.
I could record a low defintion video stream of only 50k per second and then I would be able to get about 26 hours on the same DVD.

Petaluma is correct. You can buy T180's and T200's for American VHS players. Most of them are labled "Professional", but they are still just VHS tapes, available to anyone and will work in any American VHS machine. The T180 has 9 hours on extended play and the T200 has 10 hours in that mode.