Basque is a very interesting language. Some people think it is language of Cro-Magnon Man. I have also read it could be related to Navajo, Apache, Inuit, Georgian, and Ket.
Basque has also been linked to Ancient Egyptian.
There is the so-called Dene-Caucasian hypothesis which groups Basque with other languages.
Here's one version from the Wiki article:
1. Dene-Caucasian languages [8,700BCE]
1.1. Na-Dené languages/Athabascan-Eyak-Tlingit
1.1.1. Athabaskan-Eyak
1.1.1.1. Athabaskan
1.1.1.2. Eyak
1.1.2. Tlingit
1.2. Sino-Vasconic languages [7,900BCE]
1.2.1. Vasconic (Basque)
1.2.2. Sino-Caucasian languages [6,200BCE]
1.2.2.1. Burushaski
1.2.2.2. Caucaso-Sino-Yenisseian [5,900BCE]
1.2.2.2.1. North Caucasian languages
1.2.2.2.1.1. Northeast Caucasian languages
1.2.2.2.2.2. Northwest Caucasian languages
1.2.2.2.2. Sino-Yeniseian [5,100BCE]
1.2.2.2.2.1. Yeniseian languages
1.2.2.2.2.2. Sino-Tibetan languages
Navaho and Apache are in the Athabascan family. Ket and Kott are the memebers of the Yeniseian family.
According to the Russian Nostratcists and also the late Jopseph Greenberg, the Eskimo-Aleut family (of which Inuit is a part) is part of a larger grouping that also contains Indo-European, Uralic, Altaic, Japanese-Korean-Ainu, Gilyak, and Chukchee. All of these languages, with the exception, IIRC of Ainu, use an "m" sound for the first person and a "t" sound for the second person.
Some Nostraticists extend this group to include Afro-Asiatic, Dravidian, and Kartvelian (Georgian and related).