It wasn't because of anything contained within the first few episodes of Merlin - it was the reason I was watching it.
I was watching Merlin, because one of the tumblrs (or perhaps a couple) like to post entertaining Merlin gifs....and I kept seeing them, and kept seeing them...until finally I was like, "that show kind of looks entertaining - and I want to know why that dude, who was laughing in the last gif, is crying in this one...and damn it...I think I'm going to have to watch this show, I think."
And I'm not saying that Merlin is a great show - I'm finding it more entertaining than I found Hawaii 5-O, but that's me. What I'm saying is that the ONLY reason that I'm watching it is because some fan made some amusing gifs.
Now, it's true I didn't PURCHASE the show. I downloaded it, because I am broke...but, if I fell in love with the show enough, I WOULD buy it. Am I just saying that? No. I know I would buy it, because that's what happened with BBC's Sherlock.
I didn't even have a tumblr account at that point...I have

So, I found a torrent and watched the show - illegally....and then I pretty much immediately purchased myself the DVD, because IT WAS AMAZING AND I NEEDED TO OWN IT.
There's a case right there where an adorable free fanart caused me to illegally download something, which then caused me to buy a DVD that I would not have otherwise purchased because I live in Canada and I don't have cable - without the fanwork, I would never have even known that the show existed, let alone wished to purchase it. The BBC made money, because someone A)made a fanwork, and B)allowed me to view the BBC content for free so that I could SEE what they were offering.
And then today, I was listening to some playlists on youtube while I worked, because I was sick of all my music (all 8 gigs of it). A new addition to my youtube playlist is Bottom of the River by Delta Rae - how did I find it? A Supernatural Fanvid.
Actually, since 2005, I've discovered pretty much 90% of new music through fanvids. In 2005, I was big into anime, so I used to just go to youtube and type in "amv" and watch whatever looked interesting from my favourite animes and then clicking on the "related videos" and exploring music that way.
Basically, what I'm saying is that without fanworks, I probably wouldn't purchasing ANYTHING (except books, because I love bookstores). Since 2002, I've only watched or listened to things that have come recommended to me by friends and family...and fanworks are fundamentally in keeping with that tradition, because to put that much time and effort into something is to recommend it. It's saying "I liked this thing so much that it inspired me to create this artwork, to write this fanfic, to make this video, to capture this part of it in a gif."
Fanworks are social marketing at it's best, in my opinion....and I think the corporations behind these TV show, movies, and music, should welcome them instead of trying to stifle them through restrictive laws and copyright.
For what it's worth, anyway.