Among all attested Indo European languages, which one best preserves the features of Proto Indo-European? Which is most useful in the reconstruction of PIE?
There are many possible answers to this question.
Historically, the comparative method was born from observing the regularity of phonological and morphological correspondences between Classical European languages (that is, Latin and Greek), Germanic languages and dialects on one hand and, on the other hand, Sanskrit and Avestan (two "oriental" languages which have been discovered and started to be learned by the Europeans only at the beginning of the 19th cent.). Therefore, the Proto-Indo-European has been initially shaped on the model of these comparanda. Sanskrit was initially considered not only the most conservative of the IE languages, but even the very Proto-language from which the others would have descended. Later it became clear that Sanskrit was conservative in some aspects (e.g. preservation of the aspirated stops), but innovative in some others (e.g. merger of the ablaut vowels into one phoneme /a/). The Proto-languages, therefore, had to be re-designed in order to reestablish the right chronology of the preserved phenomena. For the vowels, for example, Latin and espcially Greek were more trustworthy than Sanskrit. Later on, also the morphology started to be reconsidered. Were the case system of Sanskrit a perfect match of the one that we should postulate for the PIE? It is not considered obvious anymore: some cases could have been created independently in every branch of the IE family from a preexisting simpler system with less cases.
A better and more meaningful question to ask is: what are the unique IE features preserved exclusively by each of the IE branches? Sanskrit has some of them (preservation of the aspiratae, or, say, of the so-called injunctive), Greek has others (the vowel system, the position of the accent), Lithuanian has its own (the quality of the accent) etc. Interestingly, even some very "recent" IE branches can help reconstructing some very important IE feaures. Thus, Albanian apparently preserves the otherwise unattested and only presumed distinction between velar, palatal and labiovelar stops. Therefore, each branch's contribution is important for the whole picture. Speculating on which one is "more important" than others does not make much sense.
Usually, the oldest languages preserve more IE features just because they are closer to the proto-language. But this is often countered by some striking examples of conservative features preserved by a modern language. This is often used as a proof os presumed "superiority" of such languages. The most famous case is, probably, Lithuanian, which has preserved some very archaic features (the pitch accent, for example, or the nominal endings with the final -s in the Nominative). However, it is also rather innovative in some other respect. Sometimes you can hear that Lithuanian is "the PIE today", but this is a nationalistic exageration. Interestingly, at the beginning of the comparative linguistics the same was thought concerning the Germanic languages. Moreover, the initial impulse for this field was exactly the German cultural nationalism.
To be honest, I think this is a useless question. All IE languages have preserved certain features of the hypothetical parent language and have lost others. All IE languages need to be taken into account in reconstructing the proto-language. There is no objective way to determine which daughter languages have “best” preserved these features. For example, the hypothetical IE laryngeals are preserved as such only in Anatolian, but Anatolian has lost lots of other features which have been attributed to PIE.
Or to stay with living languages: Russian has a very complex system of cases, but has lost all conjugated forms of the verb except the present indicative active. Modern Greek, on the other hand, has a pruned-down system of cases, but a very well preserved verbal system (active and middle voice, aorist vs imperfect, subjunctive etc.). Which has been “better” at preserving PIE features?
While this post has already attracted quite a few really good answers, I want to touch on a different aspect that has not been directly addressed. As several others have said, older languages like Hittite, Sanskrit, Avestan, Greek, and Latin definitely have more in common with Proto-Indo-European (PIE) as they are not removed as far from the ancestral source in time, and also because PIE was mostly reconstructed in their image. A more interesting question to ask is which modern (still living and thus changing) Indo-European language is the most "like" PIE and why.
The usual answer to this is Lithuanian ― though not in all respects. Lithuanian, and Balto-Slavic languages, in general, do behave quite conservatively when it comes to nouns and adjectives ― cases (including the vocative) and all, and Lithuanian, in particular, preserves some of the morphology, as well. It also preserves the PIE pitch accent (although with some details changed). However, Lithuanian, at least dialectally, also has come up with some noun cases that were likely not present in PIE. It has also lost the neuter gender, still preserved in all Slavic languages, as well as a few others like High and Low German (Germanic), Icelandic (Germanic), Romanian (Italic), Gujarati (Indo-Iranian). In other respects, other languages have been more conservative. Modern Greek preserves the verbal morphology extremely well. Slovenian (Slavic) preserves the dual number. Most (but not all) Indo-Aryan languages preserve breathy voiced stops (
/bʱ/, plus the innovated retroflex
/ɖʱ/). Also, nearly all Indo-Iranian (IIr) languages, from Bengali and Wakhi in the east to Ossetic and Kurmanci in the west (as well as Armenian ― not IIr, but close), preserve the SOV word order found in some of the old IE languages but subsequently changed to SVO in the European branches.
The classical (and still true) answer is: The older, the better.
Gothic is better than Modern High German, Latin better than French, and so on.
Besides that, one should use as many languages as possible. To assign a certain feature to Proto-Indogermanic it should have left traces in more than one branch. Only accumulating information from several branches allows a reliable reconstruction.
Having said this, there are indeed some features that are better preserved in certain branches or languages than in others: Laryngeals in Hittite, Verbal inflection in Greek and Sanskrit, Accent in Lithuanian, Greek, and Sanskrit, Nominal inflection in Latin, Old Church Slavonic and Sanskrit.
That would be Hittite, as it is the most archaic IE language and the best attested of the Anatolian languages. It or Anatolian in general is the root in the taxonomies of Hamp from 1990, Ringe et al from 2002, Rexova et al from 2003, Starostin from 2004, and the Bayesian analysis of Gray et al from 2011. The living language most like PIE is probably Armenian, because it's the most primitive of the living languages of IE in both the cladistic analysis of Rexova et al from 2003 and the Bayesian analysis of Gray et al from 2011.
Lithuanian, Latin and Greek possibly have the most features of PIE.