How do you determine when you move from beginner to intermediate to advanced levels in strength training? What are some indicators? I'm assuming it's not how much weight is lifted, since that changes per person or overall length of training.
There are "strength standards" charts (such as this one for the squat) that one can use to get an idea of the rough weights that this usually occurs at, but Rippetoe and others have deprecated them as misleading. (They were never meant to guide individual progress or programming changes.) You are right to focus on factors other than the weight being lifted.
Demarcating The Novice/Intermediate Line
Greg hit the nail squarely on the head in terms of the bare-bones, technical definition. That's the one you should use. Phrased another way:
(Page 113, Rippetoe & Kilgore's Practical Programming)
In other words, if you can get stronger by properly recovering from a single workout, you're a novice. If not, you're on to intermediate programming. Note that this shift may occur for an individual lift instead of all lifts at once, and should be preceded by a series of deloads as well as a rigorous review of one's nutrition and sleep in order to ensure that linear gains are indeed exhausted.
Demarcating the Intermediate/Advanced Line
It's unlikely that many of us will have to worry about this in our own lifting, but the shift from intermediate to advanced programming is marked by the diminishing returns of a properly implemented weekly progression program. In these cases:
(Ibid, page 137)
The different levels, as defined by Rippetoe et. al., are defined by how close you are to your genetic potential. You're right that the amount of weight lifted is only a rough indicator of level because of individual differences. My understanding is that recovery time is a better predictor of level. For example, if you're an intermediate then you can fully recover in a week. A novice takes a day or two and is then back to full strength, even if he's moving serious iron.