I'm a new student of Latin, and not an expert on the Vulgate, so take my review for what it's worth. As far as I can tell, there are three versions of the Vulgate in print today, and I have copies of all three of them. So I thought that perhaps those who don't want to buy three versions might appreciate a neophyte's impression of their relative strengths and weaknesses. The full names on the title pages are rather long, so I'll refer to these three versions briefly as the Stuttgart Vulgate (Biblia Sacra iuxta vulgatam versionem), the New Vulgate (Bibliorum Sacrorum nova vulgata editio or Novum Testamentum Latine), and the Madrid Clementine (Biblia Sacra iuxta Vulgatam Clementinam).
The Stuttgart Vulgate is a compact one-volume digest of the big multi-volume critical editions, especially the Benedictine Old Testament and Wordsworth and White's New Testament. It comes with a critical apparatus showing the more important variant readings from the Latin manuscripts and editions. This version comes with the prologues of St Jerome, the old medieval critical apparatus of the Gospels (canones evangelorum), the apocryphal books of III and IV Ezra, Psalm 151, Prayer of Manasses, and the Epistle to the Laodiceans, as well as the protocanonical and deuterocanical books. It also contains two complete Psalters, both by St. Jerome: The Psalterium Gallicanum and the Psalterium juxta Hebraicum. The two psalters are laid out side-by-side on facing pages to facilitate comparison. This version attempts to reconstruct the experience of reading a medieval manuscript, so the spelling is medieval, which can be a problem for anyone used to the Clementine, and to anyone looking up words in a dictionary. The text also lacks punctuation: no commas, colons, periods, question marks, or quotation marks; this actually is not a major problem in Latin, which is so rich in conjunctions. However, the lack of question marks sometimes gives me pause, as when Caiaphas says to Jesus "Tu es Christus Filius Benedicti" (Mc 14,61). The text is well cross referenced, although the titles of books in the cross references are given in German rather than Latin. The typeface is modern and easy to read.
The Clementine (you can find it used under the title "Biblia Sacra, Vulgatae editionis Sixti V. Pontificis maximi jussu recongnita et Clementis VIII Auctoritate Edita") was the official Latin text of the Catholic Church from 1502 to 1979. The Madrid edition of this classic includes a great many magisterial documents, and the biblical text is footnoted also with references to magisterial documents, although the prefaces of St. Jerome are missing, along with Clement's appendix with its three apocrypha. Color maps are provided, but they are labeled in Spanish, not Latin. The orthography is fully modern, with modern punctuation and typeface, but also quite a few typos. Like the Stuttgart Vulgate, this edition has two psalters in adjacent columns for easy comparison: The traditional Psalterium Gallicanum, and the new Psalterium Pianum, a modern (1940's) translation of the Hebrew into neo-classical Latin. One of the delights of the Clementine is that it eclectically preserves some of the text from the ancient pre-Vulgate Latin versions, which reflect the early Latin liturgy of the Church.
The New Vulgate has replaced the Clementine as the official Latin text of the Catholic Church. Its New Testament and most of its Old, like the Stuttgart Vulgate, are based on a critical reconstruction of the original Vulgate text. However, in some cases the ancient text was amended to accord with the modern Greek and Hebrew critical editions. The spelling and punctuation are all modern, so in the majority of the verses the New Vulgate text is identical to the Clementine, but in the Psalms and especially in Judith and Tobit, there are significant differences. I know of two editions of the new Vulgate, the one from Libreria Editrice Vaticana, and the Nestle-Aland edition. We can expect to see much more of the New Vulgate now that its use has been endorsed in the recent encyclical Litugiam Authenticam.
The Vatican edition can be found under the title "Bibliorum Sacrorum nova vulgata editio". It contains the complete Old and New Testaments, but none of Jerome's prologues, nor cross references, nor commentary. Its critical apparatus is minimal. It seems to be designed more for use in the pulpit than the armchair. Physically, it is an excellent tome made from red leather with gold lettering, large typeface in one column with plenty of margin on thick pages. It looks magnificent on my bookshelf.
More likely to be on my bureau is the Nestle-Aland edition of the New Vulgate. It contains only the New Testament and is sold under the title "Novum Testamentum Latine". The editors provide you with a thorough critical apparatus comparing the New Vulgate with other printed Latin versions such as the Clementine and Stuttgart, mentioned above, the Sistina, the Gutenberg, and other classic editions (the Complutensian and the Wittenberg, as well as those of Erasmus, Stephanus, Hentenius, and Plantinus). Like the Madrid Clementine, this edition has color maps, but they are labeled in English, not Latin.