word choice - Difference between "run into", "come upon" and "come across"

These phrasal verbs have a similar meaning (please correct me if not):

• run into


• come across


• come upon

Are there any nuances to choose between them? For example, I might be wrong but I mostly see run into used for meeting a person unexpectedly.

Update:
My understanding of responses so far:

• come upon is not very common any more


• run into is the most frequently used one



• run into might or might not have a negative connotation (No consensus as I see it)

Perhaps working on some concrete sentences might give a better result. For example, which one would you use for (in parentheses are my first thoughts):

• Unexpectedly meeting a dangerously fierce pack of dogs on the street (run into)


• Unexpectedly meeting a very beautiful girl whom you don't know on the street (come across)


• Unexpectedly finding a book that you had lost (come across)


• Unexpectedly finding a grammar mistake in a blog that you'd love to point out (come across)



• ...

Maybe I should've mentioned stumble upon too.
By the way, sorry about the length of the post. I had to expand it to clarify the context.

Answer

In my experinece you run into people and trouble:

I ran into Betty at the store today. I haven't seen her since college!
I ran into your co-worker Bob today.
Sorry I'm late; I ran into heavy traffic.

You come across objects:

I was cleaning up the kitchen and came across that phone bill you lost.
I was looking up (something) in the encylopedia and came across this interesting tidbit.

I'm not sure I'd use either when talking about a grammar error in a blog; I'd be more likely to say I found or noticed it. I don't know why that is.