Is there a list of airports with Category 3 ILS systems?
According to my current navigation database (AIRAC 1912), the following 228 airports have a category III ILS approach to at least one of their runways:

CYVR (VANCOUVER INTL) on runways: 08L, 08R, 26L, 26R
CYYC (YYC CALGARY INTL) on runways: 17L, 35R
CYYT (ST JOHNS INTL) on runways: 11, 29
CYYZ (LESTER B PEARSON INT) on runways: 05, 06L
EBBR (BRUSSELS NATIONAL) on runways: 25L, 25R
EBCI (BRUSSELS SOUTH) on runway: 24
EBLG (LIEGE) on runways: 04R, 22L
EDDB (SCHOENEFELD) on ALL runways: 07L, 25R
EDDC (DRESDEN) on runway: 22
EDDE (ERFURT-WEIMAR) on runway: 28
EDDF (FRANKFURT/MAIN) on runways: 07C, 07L, 07R, 25C, 25L, 25R
EDDG (MUENSTER/OSNABRUECK) on runway: 25
EDDH (HAMBURG) on runway: 23
EDDK (COLOGNE-BONN) on runways: 14L, 32R
EDDL (DUESSELDORF) on runways: 05R, 23L, 23R
EDDM (MUNICH) on ALL runways: 08L, 08R, 26L, 26R
EDDN (NUERNBERG) on runway: 28
EDDP (LEIPZIG-HALLE) on ALL runways: 08L, 08R, 26L, 26R
EDDS (STUTTGART) on ALL runways: 07, 25
EDDT (TEGEL) on runways: 08L, 26R
EDDV (HANNOVER) on runways: 09L, 27R
EDDW (BREMEN) on runways: 09, 27
EDFH (FRANKFURT-HAHN) on runway: 21
EDLV (NIEDERRHEIN) on runway: 27
EDNY (FRIEDRICHSHAFEN) on runway: 24
EDSB (KARLSRUHE/BADEN-BADE) on runway: 21
EDVK (KASSEL-CALDEN) on runway: 27
EFHK (VANTAA) on runway: 22R
EGAA (ALDERGROVE) on runway: 25
EGBB (BIRMINGHAM) on ALL runways: 15, 33
EGCC (MANCHESTER) on runways: 05L, 23R
EGCN (DONCASTER SHEFFIELD) on runway: 20
EGGD (BRISTOL) on runway: 27
EGGP (LIVERPOOL) on runway: 27
EGGW (LUTON) on ALL runways: 08, 26
EGHH (BOURNEMOUTH) on runway: 26
EGHQ (NEWQUAY) on runway: 30
EGKK (GATWICK) on runways: 08R, 26L
EGLL (HEATHROW) on ALL runways: 09L, 09R, 27L, 27R
EGNM (LEEDS BRADFORD) on runway: 32
EGNT (NEWCASTLE) on ALL runways: 07, 25
EGNX (EAST MIDLANDS) on runway: 27
EGPF (GLASGOW) on ALL runways: 05, 23
EGPH (EDINBURGH) on ALL runways: 06, 24
EGSS (STANSTED) on ALL runways: 04, 22
EHAM (SCHIPHOL) on runways: 06, 18C, 18R, 27, 36C, 36R
EHBK (MAASTRICHT-AACHEN) on runway: 21
EIDW (DUBLIN INTL) on runways: 10, 28
EKBI (BILLUND) on ALL runways: 09, 27
EKCH (KASTRUP) on runway: 22L
EKYT (AALBORG) on runway: 26R
ELLX (LUXEMBOURG) on runway: 24
ENGM (GARDERMOEN) on ALL runways: 01L, 01R, 19L, 19R
EPWA (CHOPIN) on runway: 33
ESGG (LANDVETTER) on ALL runways: 03, 21
ESSA (ARLANDA) on runways: 01L, 01R, 19L
ETAR (RAMSTEIN AB) on runway: 26
GMMN (MOHAMMED V INTL) on runways: 35L, 35R
KADW (JOINT BASE ANDREWS) on runways: 01L, 19R
KAFW (FT WORTH ALLIANCE) on runway: 16L
KATL (HARTSFIELD - JACKSON) on runways: 08L, 09R, 10
KAUS (AUSTIN-BERGSTROM INT) on runway: 17L
KBDL (BRADLEY INTL) on runway: 06
KBGR (BANGOR INTL) on runway: 15
KBNA (NASHVILLE INTL) on runways: 02L, 02R
KBOI (BOISE AIR TERMINAL/G) on runway: 10R
KBOS (LOGAN INTL) on runways: 04R, 33L
KBWI (WASHINGTON INTL/MARS) on runway: 10
KCAE (COLUMBIA METRO) on runway: 11
KCLE (CLEVELAND-HOPKINS IN) on runways: 06L, 24R
KCLT (CHARLOTTE/DOUGLAS IN) on runways: 18R, 36C, 36L, 36R
KCVG (CINCINNATI/NORTHERN ) on runways: 36C, 36R
KDAY (COX-DAYTON INTL) on runway: 06L
KDEN (DENVER INTL) on runways: 34L, 34R, 35L, 35R
KDFW (DALLAS-FT WORTH INTL) on runways: 17C, 17L, 18R, 35C, 35R
KDSM (DES MOINES INTL) on runway: 31
KDTW (DETROIT METRO WAYNE ) on runways: 03R, 04L, 04R
KEUG (MAHLON SWEET) on runway: 16R
KEWR (NEWARK LIBERTY INTL) on runways: 04R, 22L
KFAT (FRESNO YOSEMITE INTL) on runway: 29R
KGEG (SPOKANE INTL) on runways: 03, 21
KGSO (PIEDMONT TRIAD INTL) on runway: 05L
KGSP (GREENVILLE SPARTANBU) on runway: 04
KGTF (GREAT FALLS INTL) on runway: 03
KHOU (HOBBY) on runway: 04
KIAD (WASHINGTON DULLES IN) on runways: 01L, 01R, 19C, 19R
KIAH (GEORGE BUSH INTERCON) on runways: 08L, 26L, 26R, 27
KILN (WILMINGTON AIR PARK) on runway: 22R
KIND (INDIANAPOLIS INTL) on runways: 05L, 05R
KJAN (EVERS INTL) on runway: 16L
KJAX (JACKSONVILLE INTL) on runway: 08
KJFK (KENNEDY INTL) on runways: 04R, 22L
KLAX (LOS ANGELES INTL) on runways: 24R, 25L
KLIT (CLINTON NATL/ADAMS) on runway: 22R
KMCI (KANSAS CITY INTL) on runways: 01R, 19R
KMCO (ORLANDO INTL) on runways: 35L, 36R
KMDT (HARRISBURG INTL) on runway: 13
KMEM (MEMPHIS INTL) on runways: 36C, 36L, 36R
KMHT (MANCHESTER) on runway: 35
KMKE (GEN MITCHELL INTL) on runway: 01L
KMSN (DANE CO REGL-TRUAX) on runway: 36
KMSP (MINNEAPOLIS-ST PAUL ) on runways: 12L, 12R, 35
KMSY (ARMSTRONG NEW ORLEAN) on runway: 11
KOAK (METRO OAKLAND INTL) on runway: 30
KOMA (EPPLEY) on runways: 14R, 32R
KONT (ONTARIO INTL) on runway: 26L
KORD (CHICAGO OHARE INTL) on runways: 09L, 10C, 10L, 10R, 27L, 27R, 28C, 28L, 28R
KORH (WORCESTER REGL) on runway: 11
KPDX (PORTLAND INTL) on runway: 10R
KPHL (PHILADELPHIA INTL) on runway: 09R
KPIT (PITTSBURGH INTL) on runways: 10L, 10R
KPVD (GREEN STATE) on runway: 05
KPWM (PORTLAND INTL) on runway: 11
KRDU (RALEIGH-DURHAM INTL) on runway: 23R
KRFD (CHICAGO/ROCKFORD INT) on runway: 07
KRIC (RICHMOND INTL) on runway: 34
KSDF (LOUISVILLE MUHAMMAD ) on runways: 35L, 35R
KSEA (SEATTLE-TACOMA INTL) on runways: 16C, 16L, 16R
KSFO (SAN FRANCISCO INTL) on runway: 28R
KSLC (SALT LAKE CITY INTL) on runways: 16L, 16R, 34L, 34R
KSMF (SACRAMENTO INTL) on runway: 16R
KSTL (ST LOUIS LAMBERT INT) on runways: 11, 12L, 30R
KSWF (NEW YORK STEWART INT) on runway: 09
KTPA (TAMPA INTL) on runway: 01L
LBSF (SOFIA) on runway: 27
LDZA (FRANJO TUDMAN) on runway: 05
LEAS (ASTURIAS) on runway: 29
LEBL (JOSEP TARRADELLAS/EL) on runways: 07L, 07R, 25L, 25R
LEGE (GIRONA) on runway: 20
LEMD (ADOLFO SUAREZ MADRID) on runways: 18L, 18R, 32L, 32R
LEPA (PALMA DE MALLORCA) on runway: 24L
LEVD (VILLANUBLA) on runway: 23
LEVX (VIGO) on runway: 19
LEZG (ZARAGOZA) on runway: 30R
LFBD (MERIGNAC) on runway: 23
LFBL (BELLEGARDE) on runway: 21
LFBO (BLAGNAC) on runway: 14R
LFBP (PAU/PYRENEES) on runway: 31
LFJL (METZ-NANCY/LORRAINE) on runway: 22
LFLC (CLERMONT-FERRAND/AUV) on runway: 26
LFLL (SAINT EXUPERY) on runways: 35L, 35R
LFML (MARSEILLE/PROVENCE) on runway: 13L
LFOB (TILLE) on runway: 12
LFOK (VATRY) on runway: 10
LFPG (CHARLES-DE-GAULLE) on ALL runways: 08L, 08R, 09L, 09R, 26L, 26R, 27L, 27R
LFPO (ORLY) on runways: 06, 24, 25
LFQQ (LESQUIN) on runway: 26
LFRB (BRETAGNE) on runway: 25L
LFRS (NANTES/ATLANTIQUE) on runway: 03
LFSB (BASLE-MULHOUSE) on runway: 15
LFST (ENTZHEIM) on runway: 23
LHBP (LISZT FERENC INTL) on runways: 13L, 13R, 31R
LIMC (MALPENSA) on runways: 35L, 35R
LIME (ORIO AL SERIO) on runway: 28
LIMF (CASELLE) on runway: 36
LIML (LINATE) on runway: 36
LIPE (BORGO PANIGALE) on runway: 12
LIPO (MONTICHIARI) on runway: 32
LIPX (VILLAFRANCA) on runway: 04
LIPZ (TESSERA) on runway: 04R
LIRF (FIUMICINO) on runway: 16R
LJLJ (BRNIK) on runway: 30
LKMT (MOSNOV) on runway: 22
LKPR (RUZYNE) on runway: 24
LOWG (GRAZ) on runway: 35C
LOWK (KLAGENFURT) on runway: 28R
LOWL (LINZ) on runway: 26
LOWS (SALZBURG) on runway: 15
LOWW (SCHWECHAT) on ALL runways: 11, 16, 29, 34
LPPT (LISBON) on runways: 03, 21
LROP (HENRI COANDA) on runways: 08L, 08R
LSGG (GENEVA) on runway: 22
LSZH (ZURICH) on runways: 14, 16
LTAC (ESENBOGA INTL) on runway: 03R
LTBA (ATATURK INTL) on runway: 05
LTFM (ISTANBUL) on runways: 16R, 17L, 34L, 35R
LYBE (NIKOLA TESLA) on runway: 12
LZIB (M.R. STEFANIK) on runway: 31
MMTO (LIC ADOLFO LOPEZ MAT) on runway: 15
NZAA (AUCKLAND INTL) on runway: 23L
OMAA (ABU DHABI INTL) on runways: 13L, 31R
OMDB (DUBAI INTL) on ALL runways: 12L, 12R, 30L, 30R
OMDW (AL MAKTOUM INTL) on runways: 12, 30
OPLA (ALLAMA IQBAL INTL) on runway: 36R
OTBD (DOHA INTL) on runway: 33
OTHH (HAMAD INTL) on ALL runways: 16L, 16R, 34L, 34R
PAFA (FAIRBANKS INTL) on runway: 02L
PANC (STEVENS ANCHORAGE IN) on runway: 07R
RJAA (NARITA INTL) on runway: 16R
RJCC (NEW CHITOSE) on runway: 19R
RJCK (KUSHIRO) on runway: 17
RJFT (KUMAMOTO) on runway: 07
RJGG (CHUBU CENTRAIR INTL) on runway: 36
RJOA (HIROSHIMA) on runway: 10
RJSA (AOMORI) on runway: 24
RJTT (TOKYO HANEDA INTL) on runway: 34R
RKSI (INCHEON INTL) on ALL runways: 15L, 15R, 16, 33L, 33R, 34
RKSS (GIMPO INTL) on runway: 14R
SAEZ (EZEIZA INTL MINISTRO) on runway: 11
SBGR (GUARULHOS-GOV ANDRE ) on runway: 09R
SCEL (ARTURO MERINO BENITE) on runway: 17L
SCIE (CARRIEL SUR INTL) on runway: 02
SCQP (LA ARAUCANIA) on runway: 01
SKBO (EL DORADO INTL) on runway: 13R
SPJC (JORGE CHAVEZ INTL) on runway: 15
UAAA (ALMATY) on runways: 23L, 23R
UACC (NURSULTAN NAZARBAYEV) on ALL runways: 04, 22
UBBB (HEYDAR ALIYEV INTL) on ALL runways: 16, 17, 34, 35
UKBB (BORYSPIL INTL) on runway: 36R
ULLI (PULKOVO) on runways: 10L, 28R
UMMS (MINSK-2) on runway: 13L
URWW (GUMRAK) on runway: 06
UTAA (ASHGABAT) on runways: 12R, 30L
UUDD (DOMODEDOVO) on runway: 14R
UUEE (SHEREMETYEVO) on runways: 06L, 06R, 24C, 24R
UWWW (KURUMOCH) on runway: 15
VECC (NETAJI SUBASH CHANDR) on runway: 01R
VHHH (HONG KONG INTL) on runway: 25R
VIAR (SRI GURU RAM DASS JE) on runway: 34
VIDP (INDIRA GANDHI INTL) on runways: 11, 28, 29
VIJP (JAIPUR) on runway: 27
VILK (CHAUDHARY CHARAN SIN) on runway: 27
YMML (MELBOURNE INTL) on runway: 16
YPPH (PERTH INTL) on runway: 21
ZBAA (BEIJING CAPITAL) on runway: 36R
ZBAD (DAXING) on runways: 01L, 35L
ZHHH (TIANHE) on runway: 04R
ZSPD (PUDONG) on runway: 34L


Trivia: only about 19% of all airports in the database have some ILS at all and only about 9% of them have a Cat. III ILS:



And this is the geographic distribution:


Map generated by the Great Circle Mapper