At altitude, you can often clearly see the rotation, as the vortexes grab the contrails. They persist for quite some time, not just seconds, but often minutes. They also drift downwind, and tend to descend.
When you encounter one laterally (i.e. you cross it), it will give the aircraft a very good 'thump'. But, when you hit one from an aircraft travelling more or less in the same direction (or 180 out), you will normally only hit one of the cores, and it will give a very strong rolling moment to the aircraft. A 737 sized aircraft can easily be rolled onto its back by such an encounter.
The 757 was renowned for producing wake turbulence out of all proportion to its size.
Whilst flying a bigger aircraft makes you less susceptible to the nasties, you are't immune. I recall chatting to one of our 747 pilots, who made the comment that he'd hit our wake, and that it wasn't nice, and I ran into a Singair 380s wake just after take off in Singapore, and even the big fella reacted to it. Having said that though, it's more an inconvenience for the big aircraft, but is very dangerous for the smaller aircraft.