Students of historical linguistics tend to be restricted to a single language family, such as Indo-European. It's a shame, because Proto-Indo-European (PIE) was spoken geographically close to several other important language families: to the north was Proto-Uralic (PU); to the south (in order of closeness): Proto-Northwest and Proto-Northeast Caucasian (PNWC & PNEC respectively), Proto-Kartvelian a bit further down (PK), then Hurro-Urartian, Hattic in Anatolia, Sumerian and Akkadian in the Fertile Crescent, then Elamite in modern-day Iran and Canaanite languages in the Levantine strip.
Even though these languages are unrelated (or at least, no relationship has yet been demonstrated), chance and contact has made several of the families unusually similar. The Caucasian language families - Northwest Caucasian, Northeast Caucasian, and Kartvelian - share loanwords with Proto-Indo-European. But beyond mere loanwords, one aspect of unusual closeness is the phonological systems.
|Monophthong phonology of...|
1 = Restricted reconstruction of PIE where the outliers and unusual vowels are ommitted. In the Leiden School, only short vowels *e and *o are accepted during Early PIE and only arose late.
2 = Expanded reconstruction where all traditionally reconstructed vowels are included, even the highly controversial candidates.
3 = Controversial.
4 = Dubious.
Though the languages around the Caucasus are often characterized as being similar, it's quite clear from the list that there was a good deal of diversity. At a first glance, only PK and b.PIE have an interesting degree of similarity in my opinion, and further exploration into their phonotactics would reveal those similarities to be more due to chance and contact than a pedigree.
a.PIE from "Proto-Indo-European" on Wikipedia.org.
b.PIE from From Proto-Indo-European to Proto-Germanic by Don Ringe. Oxford University Press. (2006).
PNWC from A North Caucasian Etymological Dictionary by S. A. Starostin & S. L. Nikolayev. Asterisk Publishers. (1994).
PNEC from A North Caucasian Etymological Dictionary by S. A. Starostin & S. L. Nikolayev. Asterisk Publishers. (1994).
PK from "Proto-Kartvelian" on Wikipedia.org.