I'll share some experience with your from cornify.com, which had the same effect and still goes strong 1.5 years later (this year invitation to ROFLCON, SXSW people's choice award, installed in 550000 web pages...). This is my experience with a project that's different from yours, so I hope it will help with your specific situation.
The main thing you need to achieve is to make your site about a bigger theme. This feature will remain the core, but you need to be associated with something bigger. With Cornify, it's always been about happiness. Unicorns and rainbows are (almost) second to that, which gives me much more room to work with. Make your site about famous writers, becoming a better writer, or something like that. Use imagery that matches the theme.
The second big thing is to make your tool deep, while keeping it simple. People know it for this one thing and the one thing only. Make it so you can find something new every time you use it, make it smart so it learns with the number of times you use it. Surprise people. Tweak, tweak, tweak.
Third recommendation is to build a voice and talk to people. Get Twitter and Facebook accounts. Decide on how you want to relate to people and what they should get out of being interested in you. I've gotten so many "Oh, I can't believe Cornify is on Twitter" comments, it shows that you care about the site. A brand would also be a big help. Maybe you can look into using imagery of famous writers.
Find a way that people can create things on your site. With Cornify, people really like the photo uploader. Find something that people can create on your site and then share. This keeps people coming back.
Most importantly, keep things fun. This is not serious business, this is a meme. If things stop being fun or get cluttered with ads, people will not take your serious and won't come back. Be very careful about monetizing. A meme that people like is an incredibly thing to have in your resume and a great talking point. I worked on projects for MTV, Nintendo, EA, etc, but people get way more excited when they find out I created Cornify. This is a meme and you may be more proud of other things you have done, but in terms of public recognition, you should take this very serious.
And congratulations. It's very exciting to see a project blow up like this. Hope you have a great time with it.