There's a lot of reasons behind disallowing just any foreign volunteers, mainly security, logistics and the fact that it isn't really needed. We don't see the grand wars and such. However, there is still foreign elements allowed in some areas the best known probably being the French Foreign Legion (WikiAcutal Site). They are comprised primarily of foreigners, however some French nationals do get in by usually claiming Swiss citizenship or another nearby state, and their officer hierarchy is comprised mostly of French nationals with few enlisted Legionnaires making it to an officer rank. They are used pretty much freely by the French and are deployed whenever the French want to have a presence. Most recently in Mali. There's an unofficial motto that is "Foreign Blood before French Blood", I believe they mention it in "Legionnaire" (More info below).

Additionally, multiple countries still allow foreigners in either a Legion-esque way or into the actual national military (List)

If you are interested in learning more from a POV perspective about the FFL, I recommend:

Legionnaire A good read about a Legionnaire in the 60's

Well it has not changed, maybe just the volume. For example in the Croatian war of independance in 1991-1995 (hope it doesn't break 20 years rule) there were about 500-650 foreign volunteers fighting for the Croatian side alone. I can't find some source that could be considered impartial by every aspect, but I hope the website of the volunteers themself might pass? http://www.usddr.org/

Acording to their own statistics on the website there were 507 foreigners volunteering for Croatia side, out of which 90 were wounded, and 76 KIA (names of deceased, if they are known, are provided on the webpage) There were for sure also foreign volunteers on other sides in the conflict, especially in Bosnia (reports of some numbers of Russians fighting for Serbs, Middle-Easterners for Bosnians) but I can't provide sources