I'm in the U.S. on a K-1 fiancé visa, which I've read is good for only one entry into the United States. But to get ready for the wedding, a friend of mine wants to take me shopping in Toronto, Canada. Someone told me that that's okay, that I can come back again based on my fiancé visa. Is that true?
For once, the rumors are true: Although the K-1 visa is single entry, its holder can take advantage of a concept called "automatic revalidation." That means that you can take a short trip – of up to 30 days -- to either Canada or Mexico, without having to give up your I-94 when you leave.
But you'll definitely need to take a copy of your Form I-94, as well as your passport. (For extra safety, make copies of both and leave them with a friend in the U.S.) So long as you are within the time limit on the I-94 when you ask to come back, and haven't become inadmissible to the U.S., you should be allowed reentry for the balance of the time remaining on your I-94.
This possibility comes from the U.S. Code of Federal Regulations, at 22 C.F.R. Section 41.112.
Any time you leave the U.S., however, you are taking a risk. A U.S. border official could be unfamiliar with this provision of the law, or not believe that you're still planning to get married, or could decide that you have become inadmissible. Consult an experienced immigration attorney for a personal analysis.
Also, you didn't mention which country you are from, but if it's among those that the U.S. considers to be "state sponsors of terrorism," you will be ineligible for automatic visa revalidation. As of late 2016, that list included Iran, Syria, and Sudan.
For more information, see K-1 Fiance Visas.