Hapax Phonoumena

[Chuma]

Here in Northern Sweden, there's the rapid-inhalation-sound meaning "yes", to add another to the odd interjections.

Trying to think of other Swedish examples - there are some sounds that are only found in loanwords, so for example "browser" has both [R] and the fairly unusual [au]. Language authorities suggest webbläsare "web reader", which ironically also contain an exotic phoneme, [w]. Then there's the long front [a:], only found in aha and some foreign names, that I can think of.

We also have unique letters - the German ü is basically only used in the word müsli (and some names). I guess English has a similar situation in "naïve", although you might not count that as a separate letter.

[Kohorik]

Then there's the long front [a:], only found in aha and some foreign names, that I can think of.

Also in fan!

[Alon]

In Russian, the sound represented by the letter ы, [ɨ], is in complementary distribution with /i/ (it occurs only after hard consonants), with one exception: in the name of the letter, it occurs as [ɨ], while the name of the letter и is .

[jal]

In Dutch, long vowels only occur in French loans, e.g. [bɛːʒə] (which incidently also has an otherwise foreign [ʒ]). Dutch [w] only occurs syllable final* after front vowels, and isn't particularly rare there, but it's unclear what it's an allophone of, if any. I can't think of another rare phoneme that isn't (part of) an interjection or a loan.
*Note that syllabification of intervocalic consonants is a tricky thing in Dutch, and I won't touch it here.


JAL

[Nortaneous]

In Russian, the sound represented by the letter ы, [ɨ], is in complementary distribution with /i/ (it occurs only after hard consonants), with one exception: in the name of the letter, it occurs as [ɨ], while the name of the letter и is .

and placenames. Ыгыатта, Ыллымах, Ымыяхтах, Ыныкчанский

[Qwynegold]

"browser" has both [R] and the fairly unusual [au].

Do you mean voiced uvular fricative??

Language authorities suggest webbläsare "web reader", which ironically also contain an exotic phoneme, [w].

Okay, W is a letter and not a phoneme. It's pronounced [v~ʋ].

[Curlyjimsam]

/x/ is arguably one for me in English - I think I only have it consistently in loch.

[mèþru]

I though most native speakers outside of Scotland and Ireland pronounce all instances of voiceless velar/uvular fricatives as /k/ or /h/, like with German names. Besides loanwords from Celtic languages and German, there is also the infamous Hanukkah/Chanukah and chutzpah from Yiddish. Ever worse, for Hebrew speakers, is English khaki, which is pronounced with a /k/, like the Hebrew word for poop. English speakers tend to nativise loanwords.

[Vijay]

Ever worse, for Hebrew speakers, is English khaki, which is pronounced with a /k/, like the Hebrew word for poop. English speakers tend to nativise loanwords.

Khaki is from Hindi/Urdu. Speakers of that language tend to pronounce that sound as [kʰ].

[Whimemsz]

(Most dialects of) Ojibwe only have /h/ in a handful of interjections, e.g. ahaaw, "okay;" haawn!, "fire! go!"; hay' "darn it! (after making a mistake)". The last two also have unique clusters, /wn/ and /jʔ/. Some dialects have additional onomatopoeic words with /h/, e.g. Odawa/Eastern Ojibwe waahoonwe(nh), "whippoorwill"

[mèþru]

In Hebrew, חאקי khaki is pronounced with a back fricative (velar, uvular or pharyngeal depending on the speaker, but most pronounce it as a uvular): /χa.ki/

[Whimemsz]

(Most dialects of) Ojibwe only have /h/ in a handful of interjections, e.g. ahaaw, "okay;" haawn!, "fire! go!"; hay' "darn it! (after making a mistake)". The last two also have unique clusters, /wn/ and /jʔ/. Some dialects have additional onomatopoeic words with /h/, e.g. Odawa/Eastern Ojibwe waahoonwe(nh), "whippoorwill"

Oh, also, Eastern Ojibwe has /l/ only in loan words, except for one onomatopoeic bird name: kookoolii, "bobwhite"