I can see "it rained little" being used as a way to emphasize an unusually small amount of rain, as cuchuflete suggested. "It rained little" does not mean "it rained lightly." It means "it rarely rained."
"We traveled to the Olympic rainforest in western Washingon state while on vacation this year. Although this is the wettest place in the United States, with an average rainfall of over 100 inches per year, it rained little while we were there. We were surprised!"
To say "it rained a little while we were there" in the sentence above would not make sense. It would not be surprising that it rained a little while we were visiting a rainforest. It would be surprising if it rained litle, though, or more casually spoken as "only rained a little."
Thinking about this a bit more, it does sound a little stiff to say "it rained little". I think I would probably write, "we had little rain while we were there."
Hmm.. I don't see "it rained little" as "very small quantity." I see it as "very rarely rained."
For example, I could say, "When we were in the desert in Mexico, it rained little, but when it did, it poured buckets!" This is not self-contradictory, in my opinion. It rarely rained, but when it did, there was a great deal of rain.
I agree that it does not always include the implication of being surprising. I hope I didn't mislead anyone in my previous post. I only meant that having it rarely rain in a rainforest would be surprising, while having a little rain fall while in a rainforest would not.
It rained little is, as suggested, not very common.
Apart from that, I feel the difference between the two is very much as Siberia explained - and it is a difference of expectation, not of fact. A bit like the difference between half-full and half-empty. It might be clearer if I use different expressions.
It rained a little = It rained a bit.
It rained little = It didn't rain much.