I've worked at two very large companies as a mechanical engineer (currently at a consulting engineering firm). One in consumer electronics, the other in energy manufacturing. Both were relatively similar in progression schedule.
The first company had basically 7 roles on the Technical career track. The top two were kind of honorary titles for people who had made technical history with the company. So basically 5 roles from Jr Engineer to Principal Engineer, although they had their own names for them. They are basically the equivalent of Jr Engineer, Engineer, Senior Engineer, Staff Engineer (if you think of Staff as higher than Senior, I've seen it reversed. Basically Technical Lead), Principal Engineer.
The second company had around 10 levels on the technical track. It was similar to big_slacker's scale, with Engineer 1 being a junior role, 2 being between Jr and Engineer, 3-5 being an Engineer, 6-8 being a Sr Engineer (often with technical leadership or publishing), and 9 and 10 being Principal roles.
Both had very quick progressions to a mid level if you were a great performer. If you worked hard and had aptitude, you would make Sr Engineer (at the first company) or Engineer 5 (at the second company) in 3-5 years straight out of college. After that, it slowed down and you basically had to make a choice for project management/people management/technical track. From there I didn't see a pattern - or I wasn't there long enough to see one. I'm in my late 20s.
If you weren't a great performer, you stalled at Engineer (first company) or Engineer 2/3 for a while. They would try to keep you there with as little increase in pay for as long as possible. I can understand this mentality. Most managers will think of everyone but their star performers as replaceable. It's probably not true - there are lots of efficiencies gained over time in a role, but people can also stagnate in progression if they are in one role for longer than 3-4 years, especially if they're young.
I'm curious about people mentioning a "fast track" or a "high potential" path. Was this simply a trend you noticed? Did managers simply have a mental list of people they'd noted as possible fast risers? Did managers tell people directly they were thought of as future leaders/top performers? Was this specific to new hires/young people?