I don't think there is a fixed amount of time in the definition of long exposure, but I'd go with something involving "blur" as you mentioned. Just keep in mind that "blur" is subjective and can be a quite important part of the picture, or maybe "unintended blur" would be a better criteria for the definition.
If you take panning (following you subject with the camera) for example, it usually generates blur around the subject, but it is exactly this blur that make the subject more "alive". On the example below, the exposure time is not that big (0.8s) but was enough to blur the background and let the running woman float above it. This shot was hand-held (as most pannings are):
On the other hand, if you don't want the background to blur or need longer exposure times then hand holding the camera will certainly not work. But you don't need to necessarily use a tripod, just make sure the camera does not move.
For that you can use anything nearby that is stable. Here for example I used a rock on the floor for a exposure time of 3.2 seconds:
And here I used the church door to help me hand hold the camera for 0.3 seconds:
Or even the subway bench can help you... :o)
Not The Red One | Não é o vermelho http://farm6.static.flickr.com/5245/5268023139_75b1c30f25_m.jpg
The point is, keep an eye for stable supports. Carrying a tripod is helpful, but not mandatory. One important thing though (at least for compact cameras) is to make sure you turn off image stabilization before taking a shot from a stable position (and make sure you turn it back on later).
