What others have said is true. The modern tvs (i.e. not CRTs) do not show interlaced material in the same way as your tube tv.
And like others have said, the
efficiency of a tv's interlacing ability is the critical factor we are talking about; if the tv's process is sophisticated and very efficient, your eyes won't tell the difference. If the process is, let's say, not-so-efficient, you
might nail it down in some fast-moving scenes from a movie, Nascar racing, or what have you.
Having said that, I do think those who argue they can categorically see a difference are having some placebo effect going on...
BUT, as with speakers, let your
senses be the judge! We can talk about details all day, but if you cannot make out an apparent difference with your own eyes, then what's the point? Take the Pepsi challenge, and have a friend switch between 720p and 1080i (and don't peek until he/she's ready). Whatever looks best to your eyes - if you can even tell a difference - is where you "should" keep the setting!