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 .
I think LOTR and The Hobbit movies would be too boring to keep W interested. Not the story and he is free to read it whenever he wants, but the long scenic shots etc make the movie not very action packed in places.
I have never seen Avatar so I have no idea what it is even about. He has watched Avatar - The last airbender both cartoon and movie. My kids scrap over which one of them is the last airbender lol
Narnia, they have watched it but lost interest
Matrix, probably too complex to follow.
Starwars - watched a bit of one, W liked the pod racing but not really the rest of it.
Tron, don't know what it is.
TMNT, they have seen the cartoon and liked it.
I guess you just have to judge if you think it is suitable content and if your child would be interested in it. We mostly stick with the Pixar type movies and they enjoy those.
DH tried Men in Black the other day, but it turns out that has a lot of casual swearing in it so it went off pretty quickly!
DD who is 4 is guided by what we watch and what we think she can handle.
Last night she watched TMNT and has pretended to be a ninja turtle (I even had to make her a costume out of my red scarf and washing basket.
She has also seen Harry Potter and loves it!
The other movies you have listed I am not into so she hasn't seen them. I think she would be bored (I would be too as I am really not into those kind of movies LOL)!
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