When I buy something off the internet, I'd like to ask the merchant to consider accepting Bitcoin. What's the best way to explain to a merchant what Bitcoin is, and what it would do for them? Any success stories?
Probably you should approach the merchant with a group of friends, and each one of you should separately ask him over the span of a couple days a question like: "I would like to buy X from you, but I would like to pay for it in Bitcoins. I understand that this is sort of payment gives you more work, so I am willing to pay Y% more. The current exchange rate at https://mtgox.com is Z USD/BTC and going up, so will you consider selling me X for Q amount of Bitcoins?" If the merchant is small, he probably will be okay with accepting Bitcoins for a moderate transaction, you can even offer waiting a bit until the Bitcoin exchange goes through (or say, a down-payment, so the merchant will know how this thing works before committing to anything). You would probably need to follow up a bit on that inquiry explaining some things about Bitcoins, but not including all the details on how the coins work probably works in your benefit (your email doesn't look like soliciting, but as a more genuine inquiry).
A bigger merchant will probably say no (unless they are tech-savvy), but after a couple people would ask about payment in Bitcoins, the lost opportunity costs would start adding up.
Generally, you can try convincing merchants with some benefits of Bitcoin technology, but probably nothing works better than money incentives and business opportunities.
(note: method not tested)