I guess it depends on your children.
Mine are kind of weird and old fashioned, they watch Loony Tunes and Garfield on TV and I wouldn't put most of the stuff you have listed on for them. DH watched the last 3 Star Wars with them but DS2 came and hung out with me instead of watching when it started to get a bit dark.

LOTR & The Hobbit - not until they have read the books or left home (whichever comes first).
Narnia - See LOTR
Matrix - not until high school.
TMNT - They have seen have a few episodes of the original TV series.
Tron - I think we have it somewhere because MIL bought it but sci fi bores me to tears so we've never watched it.
Avatar - no idea. I don't like sci fi so I've never seen it. Since i wouldn't want them to watch something I hadn't screened first not until they leave home.

Generally I am guided by the ratings - most of the stuff we watch is G. The boys are pretty wary of PG ratings because they don't like scary movies.
I don't see any need to let them watch movies made for older audiences - their childhood is so short and they have their entire adulthood to watch movies .