IRB (Institutional review board) : Do journals ever check? Does anyone ever check?
I have never heard of a journal checking for IRB approval. However, as @xLeitix notes, your university may care very much, since doing studies on humans without IRB approval may get it into legal issues.

And I personally know of one case where departmental colleagues initiated a scientific audit of a professor, requiring her to dig up all documentation (filled-in questionnaiers, raw data, ... and IRB approvals) for some studies they were concerned about. Everything checked out all right, but if the IRB approvals had not been there, the PI would have been in very deep doo-doo.

So: get your IRB approval, and make sure it's safe and sound, with scans and electronic backup. Keep it for the requisite number of years, even after the study has ended and been published. Inquire of your university how long that is. Given today's cost of storage, I would keep the scan around indefinitely.