This question came up recently and got me thinking about it. Are there any really fast-paced songs/tunes in 3/4 timing? I couldn't think of any. I'm sure you could play any waltz super fast, but that might not sound so good.
There are many songs that fit your description, most notably several by the Stanley Brothers that really define their characteristic sound: "The fields have turned brown" and "It's never too late" spring to mind. Another fine example is Joe Val's version of "Sparkling brown eyes."
The question depends an what you define as really-fast paced.
Of course at some point they can become perceptively more a compond meter (6/4, 12/8...). Of course 6/8 jigs are very fast 3s. Like Mooo mentioned in blues. Another familiar popular example, Animals "House of the Rising Sun"; the Beatles "Norwegian Wood" example that sits in the middle, which gives, fast 3/4 or slow 6/8 debate.