Is it a pagan practice for two (or more) people to clink glasses together (e.g. when making a toast)? Do any Biblical or Talmudic sources discuss this practice?
The Minchas Shmuel pg.251 cites Shu"t Mevaser Tov 2:79 who writes that this practice of clinking galseses together seems to be a tradition of the non-Jews. As we find in Amos 6:6 "השותים במזקרי יין" and the Gemara in Shabbas 62b explains the word מזקרי means to throw wine from one cup to the other (clinking glasses could be inferred).
The Minchas Shmuel continues:
Even though we can explain a rational for this custom based on the fact that there are five senses (taste,smell,hearing,touch,and sight) when one takes a cup of wine they are only using 4 of their senses and the sense of hearing is left out and that may be a reason to clink glasses.
However,this makes sense for non-Jews who do not recite a blessing,Jews who do make a blessing in fact have all five senses since the bracha is made out loud. We therefore are not allowed to practice this custom and instead we are noheg like are ancestors to say the word L'Chaim(which also fulfills the 5 senses) which has the same gematria as minhag.
I know of no traditional Jewish source on this topic (and would be happy to see one, if anyone else does) but there is this:
Personally, I consider Snopes pretty reliable in general, though I didn't look into the sources they cite on the bottom of this article.
Short version: Clinking glasses was added (relatively recently) to toasts in order to engage hearing into a celebration that already included the other 4 senses. Additionally, it is to physically emphasize ones participation in the toast and the cohesiveness of the group.
First off, welcome to Mi Yodeia, and I hope you enjoy your stay here.
They may be onto something, Ploni. According to Wikipedia:
The International Handbook on Alcohol and Culture says toasting "is probably a secular vestige of ancient sacrificial libations in which a sacred liquid was offered to the gods: blood or wine in exchange for a wish, a prayer summarized in the words 'long life!' or 'to your health!'"
The reason i heared from a historian in middle age historie is that the clinking of glases is a custom that came as when the Lords where drinking wich each other they where afraid that they poisened the wine so by clinking some wine was spilled over from one cup to the other and so they would drink it knowing thatb there was no poison in.
Expanding upon Alain G.'s answer:
While visiting Germany, locals told me this practice developed out of fear that one's drink was poisoned. To ensure the same fate for all, people would clink glasses together hard enough for their drinks to spill into each other's glasses thereby mixing any poison present amongst all parties.
Assuming that understanding, it may be prohibited to suspect one's friend of poisoning one's drink (לחשוד בכשרים) unless one's "friend" gave one just cause for suspicion. Nevertheless, if one was justly suspicious, one may be within one's right to clink glasses in the hopes of poisoning one's "friend" based on the principle of self-defense (הקם להורגך השכם להורגו).
If a reason cannot be ascertained, it may nevertheless be prohibited to clink glasses so as not to abide by Darke'i Ha'emori (i.e. inexplicable gentile customs).