There are exceptions, but only if there is signage or road markings. For example, if there are two or more lanes marked for right turns, then obviously you can turn from any such lane.
(A little-known fact about that: most California drivers are aware that you're allowed to turn right on a red light after making a full stop, unless there's a "no right turn on red" sign - but few seem to know that this rule applies to all the lanes marked for right turns, not just the rightmost lane.)
Most bike lane markings change from a solid white line to a dotted line about 200 feet from a corner, to give drivers a hint to merge into the bike lane before turning. But even if the line doesn't turn dotted, drivers are still required to merge into the bike lane unless there is a specific indication otherwise.
However, the majority of drivers seem to be unaware of this rule and turn right from the auto traffic lane, creating the risk of a "right hook" collision, which the law is intended to avoid. I've actually had other drivers honk at me when they were waiting in a line of cars to make an illegal right turn from the auto lane while I made a legal and proper turn from the bike lane.
The San Francisco Bicycle Coalition has an excellent info page about this:
http://www.sfbike.org/news/bike-lanes-and-right-turns/
Laws on this do vary in other states. But at least in California, if you see a driver merging into the bike lane before turning right, it's not because they are a terrible driver, it's because they are following the law and (hopefully) increasing safety for bicyclists.
What's more concerning is that my state (Texas) seems to have a lot of vagueness around the laws.
Well, that's confusing to say the least.
If you still don't see the difference, here's one way you can tell. If you are stopped, waiting at the intersection, if you've merged, then you'll be occupying the bike line while you're waiting.
Human drivers are terrible.