I've recently published a paper. It's available online, but not published on hard copies yet. What should I do If I find out that there is a typo (repeated many times) in a recently published paper of mine at Elsevier?
There are two pieces of information missing in your question, but it might be better to consider each case anyway, so that my answer might help others. The first thing is whether the typo may lead to misinterpretation of your work, is an error in formulas, or anything that will harm the scientific meaning of your work. The second thing is whether you or the publisher introduced it.
If the typo is not misleading in any way (e.g. embarrassing but harmless spelling error), it is probably not worth doing much, whoever made the mistake. If the preprint version of your article is on your web page or on a repository, you should ensure it is free from the typo, and you might want to point out that the published version has this typo, but I would not see the point of going further than that.
If the typo is actually harmful, may cause misinterpretation of your work or may make it partly unintelligible, then who made the error is more important. In any case, contact the publisher and the chief editor to see how to handle it. Of course, if you did the error, you have to be apologetic while if the publisher did, you can be more demanding. The most probable outcome is that an errata will be issued. Most journals have only one version of each article, and thus cannot afford to change anything between electronic publication and print publication; however strange it may seem I saw many errata being printed in the same issue than the article they correct. Maybe electronic born journal are in a position to handle this better.
For the story, my very first article got published (both electronically and in print) with a repeated "typo": half a dozen of $n/2$ and $(n+1)/2$ where replaced by $n^2$ and $(n+1)^2$. I realized that when I received the offprints, and could not believe it. I knew I did not made the mistake, but at first I thought I did not checked the galley proofs closely enough. It turned out that the typos where introduced after the galley proofs. This made a strong case, and a corrected version of the article was reprinted entirely in a subsequent issue.
I think it fair to mention that the publisher was Springer, but I have heard similar horror stories from most big, expensive commercial publishers.