I know that there are certain pairs of countries (which do not get along with each other) where a traveller will not be permitted into one country if they have a stamp in their passport from a visit to the other country.
Considering the history of Armenia and Azerbaijan I'm wondering if these two are such a pair of countries? I was in Armenia last year and I'm considering visiting Azerbaijan this year while I'm in Georgia.
Here's some first hand experience (I visited the region a few weeks ago). Visiting Armenia is not a problem for Azerbaijan, nor is it the other way around. What is a problem, is having a visa for Nagorno-Karabakh (NKR) in your passport when you want to visit Azerbaijan. Indeed, at best, you will not be let in to Azerbaijan.
It is said that NKR has no problem issuing the NKR visa on a separate piece of paper, so that you can visit Azerbaijan afterwards, but I can not confirm that.
According to this blog, you should try to avoid visit both countries with the same passport. If you get two passports (Israel and USA, for example), try to get into one country by one of them, and to other with other passport (as author of the blog did).
The main problem is possible visiting of Nagorno-Karabakh Republic. It is a crime in Azerbaijan (illegal border crossing), so even if you were in the NKR, don't say a word about that. They can't prove anything without your words. Be careful and good luck.
Actually visiting Nagorno-Karabakh Republic is a crime in Azerbaijan, but you won't get in any kind of problem in Armenia because of visiting Azerbaijan.
I visited Armenia with a friend who had an Azerbaijani visa in his passport and in Armenia they asked a couple of questions regarding his visit from Azerbaijan in front of us, then they let him go (I'm an Armenian from Iran and my friend is Iranian.)
