As a matter of fact, there still are a number of linguists believing that some or all of the families considered to belong to the putative Altaic stock are related one way or another.
"Core Altaic" and "Extended Altaic"
The traditional "core" members were Turkic, Mongolic and Tungusic, with Japonic and Koreic being added in more recent decades. As to Uralic, to my knowledge, none of the proponents of the Altaic hypothesis believe it belongs to the putative stock.
The so-called Ural-Altaic hypothesis is now considered dead even by Altaicists, who consider Uralic either similar due to areal convergence, or related only very distantly, perhaps within the even more controversial Nostratic superstock.
"Eurasiatic" & "Nostratic"
Whether the families included in Altaic form a standalone taxon or not, proponents of the so-called "Nostratic" hypothesis, or a very similar "Eurasiatic" hypothesis, seem to believe that most or all of them belong to a larger stock together with at least Indo-European, Uralic, and depending on the version, variously also Kartvelian, Dravidian, Eskimo-Aleutian, Chukotko-Kamchatkan, Yeniseian, Nivkh, and even Afro-Asiatic, which is by some proponents considered its sister rather than mere daughter.
"Trans-Eurasian" as the most recent work
I think it was Martine Robbeets, a firm believer in the unity of the various Altaic families, who first coined this less-worn name for the hypothetical stock. Hence, Trans-Eurasian is probably what you should try and look up if you want to find the most recent work on Altaic. Some of her papers can be found on-line, e.g. Swadesh 100 on Japanese, Korean and Altaic (2004) [PDF]. An interesting discussion can be found in Transeurasian Verbal Morphology in a Comparative Perspective: Genealogy, Contact, Chance (2010) [Google Books]. See also her bibliography here.
Summary and Where to Look Next
Contrary to what @cyco130's answer suggests, there are widely accepted families that prove that historical linguistics can go, at least, twice as deep as just "a couple of millenia", and the temporal ceiling itself is a matter of controversy, which might also be one of the reasons why the Altaic debate is far from settled now. On the other hand, @cyco130 is also definitely right in that the evidence for Altaic is simply not sufficient and quite imperfect at the moment, and until the adherents make a major breakthrough (if they ever do), it is certainly safer and more correct not to lump the families together (unless you emphasize that you are using the label as a short-hand only). After all, areal convergence is just as interesting and worth investigating as genetic relationships.
Now, to direct you to some further information, I have just come across this blog article (now a dead link, but available via Wayback) that gives a nice summary. Some of the most recent critiques that can by no means be neglected have been written by Alexander Vovin (an expert especially on Japonic and Koreic) and Stefan Georg (and expert on Turkic, Tungusic and Mongolic, among other things). To be sure, some of the criticisms have been addressed or replied to, especially by G. S. Starostin & A. V. Dybo's In Defence of the Comparative Method, or The End of the Vovin Controversy (2009), or G. S. Starostin's Review of: Koreo-Japonica. A Re-Evaluation of a Common Genetic Origin. By Alexander Vovin. (2010), but it would appear critical views are prevailing.