Having struggled for most of my teen years with the issue of "are magic and fantasy inherently evil", I would like to say that while certain aspects of stories like Narnia, Lord of the Rings, the Final Fantasy series (Kingdom Hearts incl.) and just about any other fantasy series you can think of COULD be considered objectionable, one has to remember that it IS fantasy, eg it isn't real.
That said, fiction is only harmful when it encourages you to ignore the things that are important. Remember "Rack, Shack and Benny"? (y'know, from Veggie Tales). It wasn't that the chocolate Bunnies themselves were evil, it was that everyone forgot that bunnies are nice, but God is what is most important. If fantasy is making you think "ooh, I wanna try that there firaga spell! *concentrate concentrate*" then you should probably take a break from it. However, fantasy can be an enjoyable past time, so long as you remember the real world and don't go TOO far into fantasy
As someone also said, pray about it. God knows all the answers, and he also knows what is a good limit, if there is one. In fact, just praying in general is a good idea. I know it's sometimes more convenient to ask semi-strangers in an online forum (because you get quicker results) but we don't know exactly what is RIGHT for you like God does
And as for the parents issue... I didn't really figure this out until a few months ago (and lol, I'm 20), but your parents aren't out to get you or shelter you. Just because they don't understand or "approve" of a hobby of yours doesn't mean its "wrong." Because, even though you should honor them and respect them, your parents are not perfect and they're not always right. If something is really important to you, talk to them, maturely and calmly. When I was your age, I had to explain Inuyasha to my parents. They immediately went "OH NOES REINCARNATIONS AND DEMONS, THIS IS A SINANIME," but after some explanation of what the series is really about (overcoming evil in spite of personal issues, the power of team work, you're not alone, etc) they were a lot more understanding - and have even watched a few episodes with me... which, after some wheedling, they have admitted to liking and even watching a few times while I was away at college.
Parents can be tricky, but sometimes you just gotta realize that they're not always going to approve of what you do, and if it isn't severely detrimental to your well-being (spiritual or otherwise) then it merits explanation and discussion. And believe me, when you're honest with your parents, they are MUCH MUCH MUCH more inclined to trust you and give you greater freedom. I learned this the hard way.
as far as offensive goes, I agree that what is and isn't offensive is up to you. I find that the Final Fantasy/Kingdom Hearts series (which freaks my parents out) actually tends to lean towards Christian values. I haven't really encountered any that offend me outright (except for that-of-which-we-shall-not-speak Evangelion), as i tend to be pretty open about anime, keeping in mind that Japan and Christianity kinda don't go together (yet
). The only thing that offends me in regards to anime has to do with the fandoms and fanfiction - yaoi-pairings, taking characters out of context, blatant christain bashing, explicit sexual content (which has a bad habit of randomly manifesting in a seemingly innocent story... just BAM! you are now being exposed to porn without warning of any sort - no "there is explicit content" disclaimer or nothing) - which is why it's probably better to avoid fandoms than the shows themselves.
As for Harry Potter? To each his own, I guess. I'm not offended by it, I just think it's overrated tripe.
Wow, long post O_o