Peculiarities include
syllabic nasals,
laterals, and
rhotics, even rare long ones, which developed a vowel in all descendants except some
Slavonic; and apparently three sounds of unknown quality, called
laryngeals, which disappeared in all descendants but changed surrounding vowels as evidence of their existence.
Proto-Indo-European or PIE's wider affinities are unknown, but by some linguists it is linked with Etruscan and/or Afro-Asiatic and/or Finno-Ugrian. (This is the Nostratic theory.)
The grammar resembles that of Sanskrit or Lithuanian more than any other descendant, and for this reason it is sometimes absurdly claimed that a modern Lithuanian could understand Sanskrit. They are, I'm afraid, far too different. But archaic features they share are locative and instrumental cases, a dual number, and tones. Most other IE descendants have lost some or all of these.
For example, with ekwos, the masculine word for "horse", giving rise to the familiar Latin equus and Greek hippos, and to Sanskrit asvah. This is an o-stem, like most masculines, meaning that -o- runs through the declension, between the stem and the ending:
Nominative ekw-o-s
Vocative ekw-e
Accusative ekw-o-m
Genitive ekw-o-syo
Dative ekw-o-ey or ekw-ooy
Ablative ekw-o-od
Locative ekw-o-y
Instrumental ekw-o-o
And in the plural:
Nom./Voc. ekw-o-es
Acc. ekw-o-ns
Gen. ekw-o-om
Dat./Abl. ekw-o-ibhyos
Loc. ekw-o-isu
Inst. ekw-o-oys
The nom., voc., and acc. singular are obvious to anyone who knows a bit of Latin or Greek, but some other cases have travelled a great deal to get to their classical form: e.g. Greek gen. sg. -osyo > -ohyo > -oyo > -oo > -ou.
As Muke discusses below, there was a series of labiovelar consonants including kw, but it is noteworthy that ekwos doesn't contain this. It's a sequence k-w, as shown by the fact that in the satem language Sanskrit the k shifts to a sibilant, and the w separately changes to v.
It's unknown where the case endings came from originally. If they were just postpositions (as in Japanese ga and o and ni), why are the plural endings not recognisably formed from the same singular marker plus a plural element (as in an agglutinative language like Turkish)? These fused or analytic case markings are rare outside IE.
It's also unknown how the gender system came about, because although males belong to masculine and females belong to feminine, all other words are scattered unpredicyably through masculine, feminine, and neuter in the way that makes such a pain for people studyng most modern European languages. One idea is that the -om of the neuter is originally the accusative ending, because neuter things don't usually actively do anything (see animacy hierarchy) so don't need a subject ending.