From the mid-90s to the mid-oughties I managed a mailing list for Disney Afternoon based fanfic and fan art, with screen grabs, sound grabs, and occasional other goodies thrown in. As this was early in the age of the Public Internet and at that time Disney was known for being evil to fan publications, I was very careful about what I put out there, knowing how unwise it would be to annoy The Mouse. In general, here are the rules I followed for this and all of my later fan activities:
1) Don't harm the original source's merchandisability. Meaning, don't post anything that could compete with the original source. No videos of things that are legally available on DVD or elsewhere. No ripping albums and posting them for download. I have done things that use clips and songs and screengrabs, for example music videos, but those do not compete with the original episodes or songs, and are this transformative in nature. (If the owner of the song or footage complained I would take them down, however. I'm no fool. I've also done episode transcripts, but that was after consulting with the company and getting word that that would not annoy their legal staff.)
2) Don't tarnish the image of the original source. Meaning, keep things reasonably close to the spirit of the original show. In the case of the mailing list I was running, which had subscribers at Disney.com, no activity that I would be embarassed to explain to the parents of a kid in the show's original target audience. (Which is not to say I'm a prude. Mercy no! But I'm very careful where I make naughtiness available. You don't put copies of Penthouse on the bottom of the magazine rack.)
3) Don't make money off of it. This goes back to point one. If people are making illegal merchandise, the owner of the intellectual property gets nothing, and it competes with legal merchandise that they do get a cut of. So, I don't sell fan art, I don't make T-shirts, I don't sell DVDs of my fan videos.
In theory, fan sites, fan fiction, screengrabs used in icons, fan art, all of it's illegal because it uses another's IP without perission. (Others would say it's all legal because it's transformative. This is where the lawyers earn their paychecks.) However, you also have to take enforceability and the effect of such actions into account. No company, not even Microsoft or Disney, can see what every user has saved on his or her hard drive. If it's just some screengrabs, downloaded copies of fan art, etc., and it's just for your personal use, who cares? Who is it harming? It's not like you are downloading torrents of ripped DVDs or CDs rather than paying for legal copies. It would do them no good to go after such users, and in fact it would damage their image, make them look like ogres who attack their fans. As fans of ReBoot and The Simpsons know, that can result in severe backlash in the form of bad publicity.
Also, keep in mind that fan activity, whether it's writing fanfic, drawing fan art, making a site, or just saving and printing some pictures you like to look at, benefits them. It keeps their IP in front of consumers' eyes. It's free publicity. It makes for happy fans, who buy things and spread the word. So, many companies have a policy of benign neglect. Let the fans do their thing and generate interest, and only step in when they step into the danger zone, as described above.