When can I safely use CC-BY license on arXiv? On arXiv one can license a preprint on one of the following (see also a note on arXiv on licenses):


arXiv.org perpetual, non-exclusive license to distribute this article (Minimal rights required by arXiv.org. Select this unless you understand the implications of other licenses.) 
Creative Commons Attribution license
Creative Commons Attribution-Noncommercial-ShareAlike license
Creative Commons Public Domain Declaration


For cases when it is fine to submit a paper on arXiv.org perpetual (see also Does publishing a paper on arXiv prevent me from submitting it to a non-open access journal?), when I can safely use CC-BY (Creative Commons Attribution license)?

Ideally, I would use it all the time, as it is the most permissible (=open) license, which requires attribution. (However, I used it only once, it a case where I don't intend to send it to a journal; so, except for that case, when one should (or shouldn't) be afraid of using CC-BY on arXiv?)

EDIT: Here the emphasis is on arXiv perpetual vs CC, not on choosing between CC licenses.
Using a CC-BY license on arxiv.org will be fine whenever you don't need to retain exclusive rights. CC-BY is a non-exclusive license, and you are free to grant as many non-exclusive licenses as you wish. However, you won't be able to grant a exclusive license thereafter, which is what most commercial publishers are looking for. The typical "transfer of copyright" would essentially be an exclusive license in these cases.

If you intend to publish the paper submitted to arxiv.org with an open access publisher, it should generally work with a CC-BY license. Most open access publishers require only a non-exclusive license to publish a paper, so there would be no conflict here. It may however not be possible to go to a publisher which requires either an exclusive license or a copyright transfer afterwards.

Interestingly, a copyright transfer may be less restrictive than an exclusive license in this case. In principle, it should be possible to transfer copyright even if a license have already been granted to someone else (that's how a company would buy software from another company that has already been licensed). So, why not try the following with your next paper: 


Submit it to arxiv under a CC-BY license.
Submit to a commercial publisher, and add a statement like this to the copyright transfer agreement:



  "This agreement is with the understanding that a non-revocable, non-exclusive license under the terms CC-BY has been granted to a arxiv.org."


I wonder how they'd react...