Ruffino mentions that the Sicani and Elymi, two of the three pre-Greek/Phoenician peoples of the island of Sicily, were non-IE; the third and probably last group to arrive, the Siculi, were IE speakers. As far as I know, though, trying to actually work out ancient Sicilian languages is something of a nightmare.
Eteocretan is a very poorly attested language from Crete that does not appear to be IE in origin (so little is available it's not safe to make sweeping judgments); it's often proposed that it descends from Minoan. If this is true and if Eteocretan is indeed non-IE, then Minoan would be an important extinct non-IE language. Minoan itself is present in two scripts, a hieroglyphic script and the Linear A script, neither of which has really been "cracked," so there's no particular proof that it's non-IE, which is why I don't give it top billing.
Lydian is a horrible mess and is the Anatolian odd-man-out, but to the best of my knowledge it is still generally considered an IE language. Herodotus recorded that the Etruscans themselves were Lydian settlers, but support for that theory in modern thought has never been universal.
The Minoan language of ancient Crete survives in a few fragments of a writing system known as Linear A. Linear A has not yet been deciphered, but it is believed to transcribe a different language than the later Linear B script, which is known to have been used for a version of Greek.
Some scholars surmise that the Minoan language was non-Indo-European, although the evidence is scanty either way, and until the script is deciphered, the answer will not be known.
Heck yes and I write about this stuff all the time over at Cranberry Letters.
For clarity's sake, do you mean by "historical sources" as direct mentions or do you include deducing a language's existence through indirect means? For example, Basque is a well-known language isolate of Europe that survives into modern times and was first named as "Aquitaine" by Julius Caesar, and Aquitanian inscriptions have been discovered that are an ancestral form of Basque. That's about as ironclad as you can get. There are not too many languages with such a high pedigree of documentation but here's a list:
But there are classes of language documentation. For example, direct mentions by contemporaneous authors that implies the languages are distinct and unrelated:
When a language invades a new territory, speakers that learn the new language carry vestiges of their old tongues. For example, the vegisemal counting method of French is a vestige of the older Gaulish counting method. The Gauls learned Vulgar Latin but bits and pieces of Gaulish survived, forming a Gaulish substrate in the tongue. Subrates are present in all the European languages. Some are mysterious (AFAIK no one has a clue where the substrate in Hungarian is from). But most are the vestiges of older languages that were once spoken in the area. Some of the most well known are:
You'll notice I omitted some of the classic examples in these lists. With the exception of Pelasgian, I wanted to present the most accepted non-IE tongues, to the exclusion of unclassified languages like Minoan, Eteocretan, Sicani, Pictish (probably IE though), etc...