Can I present the results of a paper that is currently under review?
The only problem of presenting results that are not published is if someone else steals the results and writes their own paper about them. (Though this probably more likely only happens with ideas that are shared too prematurely.)
It is generally considered a good thing to promote one’s own work, and one way of doing this is by giving presentations at other universities.
Even if this work is under review at a different conference, I don’t think it is problematic. When presenting a paper at a conference, you are not necessarily obliged to talk about precisely the contents of the paper. You are advertising the paper, and more generally, your own work, so that people will read it and cite it. If you have bigger and better results, then these will help with your promotion of your own work.
Of course it would be weird, though probably not wrong, to talk entirely about a different paper when presenting at a conference.
There is one circumstance where presenting results under review elsewhere would be a violation of code. This is when the conference where review is ongoing requires double blind submissions.
In such cases, there's usually a clause that asks the authors not do anything overt to violate double blind review, and presenting at a different venue (where reviewers might be in attendance) would be an overt violation.
In favour of unrestricted dissemination
After thinking about the answers provided so far and the discussion in comments, it seems to me that the point of view favouring dissemination of research results unrestricted by the double-blind peer-review process needs a stronger case. I believe that the answer can be derived from higher-level, rather philosophical, principles.
... Or is it only "good practice" not to do so [to present results under review]?
What is the purpose of developing and disseminating research results?
I am an idealist in these things and argue, that it is first and foremost the advancement of human knowledge and ultimately improvement of the conditions of the human society, as well as the world around us -- regardless of what exactly "improvement" means, I have in mind something like a wider social consensus that the change has a positive vector.
Given this stance, unless there are other considerations in the game, there is no reason which could obstruct our advancement of human knowledge, which ultimately rests on dissemination of quality results to the wider public. Of course, we should be careful and act in a good faith so as to be cautious about validity, significance and originality of our results. Peer-review process is only an auxiliary mechanism helping us to filter out ideas/results in violation of these principles, i.e., helps us to recognize and fix our own misjudgements and mistakes, as well as (in the worse case) dissemination of results not advancing knowledge of humankind, but produced for other primary purposes. After all, the ultimate metrics for the results of scientific research is not the outcome of the peer-review process, but rather the long-term impact on the society and the world around us. That is, whether other people will learn something from the results and whether it eventually helps them to build something beneficial to the society.
Unfortunately, thanks to the recent proliferation of the publish-or-perish attitude and its intertwining with the need to advance human knowledge, as well as interactions of these two conflicting forces, gradually peer-review becomes primarily a mechanism to filter bad-faith products - think plagiarism, results falsification and all sorts of other scientific misconduct. Yet, I maintain, the process of filtering should not gain a higher importance than the objective of our pursuit itself. To conclude, if executed with caution, restrictions imposed by double-blind review process should not restrict our ability to disseminate our results.