Rhätische Bahn

Vigezzina / Centovalli

SSIF (Italian) and FART (Swiss) run allstops and panoramic trains between Domodossola (IT) and Locarno (CH) in a (I think) unique arrangement: two completely independent companies (often knowing almost nothing about the other one's plans...), but tickets emitted by one of them are valid on both (you could take an A/R ticket from SSIF, doing the first trip with FART and coming back with SSIF), and no cash flows between them.

Rhätische Bahn

TiLo

TiLo - Treni Regionali Ticino - Lombardia (Canton of Ticino - Lombardy regional trains) runs international lines between Canton of Ticino and Lombardy:

• S10 Como (IT) - Lugano (CH) - Bellinzona (CH)
• S30 Malpensa airport (IT) - Luino (IT) - Cadenazzo (CH) (currently limited to Cadenazzo - Luino due to improvement works)
• S40 Como (IT) - Mendrisio (CH) - Varese (IT)
• S50 Varese (IT) - Mendrisio (CH) - Lugano (CH) - Bellinzona (CH)
• RE10 Milano (IT) - Como (IT) - Lugano (CH) - Bellinzona (CH) - Erstfeld (CH)

S-services stop in all stations, RE (RegioExpress) is a "fast regional" train. Bellinzona, Como and Varese are connected to Mendrisio without change every 30 minutes.

In the future S30 will terminate at Gallarate and S50 or S40 trains will take its path to Malpensa airport.

Rhätische Bahn

Rhätische Bahn runs regional and touristic services between Tirano (IT) and Sankt Moritz (CH).

MI.CO.TRA

ÖBB (Austrian railways) and FUC (Udine - Cividale Railway) run in partnership MI.CO.TRA regional trains from Villach to Udine through Tarvisio border.

Alto Adige Mobilità / Südtirol Mobil

Trenitalia and SAD run regional services between Austria and Italy on routes 100 (Innsbruck (A) - Bolzano (I) - Trento (I) - Verona(I)) and 400 (Lienz (A) - S. Candido (I) - Brunico (I) - Fortezza (I)). Timetables on Alto Adige Mobilità / Südtirol Mobil site

Other italian "international" services

• BLS runs trains between Brig (CH) and Domodossola (IT). Some come from Bern (CH), the Swiss capital. This is a somewhat fuzzy international service, because Domodossola is a border station (with customs), so the line is formally in Swiss, but there are 18 km and 3 stations in Italy before the actual border (and Piedmont region pays for Domodossola - Iselle service).
• Trenord runs S11 Milan suburban line between Chiasso (CH) and Milan (IT). However in Chiasso station there are "formally Italian tracks" S11 terminates on, so formally S11 trains never enter Swiss.
• Turin SFM line 3 runs till Modane (F), but again Modane has "formally Italian tracks".

TiLo

TiLo - Treni Regionali Ticino - Lombardia (Canton of Ticino - Lombardy regional trains) runs international lines between Canton of Ticino and Lombardy:

• S10 Como (IT) - Lugano (CH) - Bellinzona (CH)
• S30 Malpensa airport (IT) - Luino (IT) - Cadenazzo (CH) (currently limited to Cadenazzo - Luino due to improvement works)
• S40 Como (IT) - Mendrisio (CH) - Varese (IT)
• S50 Varese (IT) - Mendrisio (CH) - Lugano (CH) - Bellinzona (CH)
• RE10 Milano (IT) - Como (IT) - Lugano (CH) - Bellinzona (CH) - Erstfeld (CH)

S-services stop in all stations, RE (RegioExpress) is a "fast regional" train. Bellinzona, Como and Varese are connected to Mendrisio without change every 30 minutes.

In the future S30 will terminate at Gallarate and S50 or S40 trains will take its path to Malpensa airport.

Rhätische Bahn

Rhätische Bahn runs regional and touristic services between Tirano (IT) and Sankt Moritz (CH).

MI.CO.TRA.

ÖBB (Austrian railways) and FUC (Udine - Cividale Railway) run in partnership MI.CO.TRA. regional trains from Villach to Udine through Tarvisio border.

Alto Adige Mobilità / Südtirol Mobil

Trenitalia and SAD run regional services between Austria and Italy on routes 100 (Innsbruck (A) - Bolzano (I) - Trento (I) - Verona(I)) and 400 (Lienz (A) - S. Candido (I) - Brunico (I) - Fortezza (I)). Timetables on Alto Adige Mobilità / Südtirol Mobil site

Tende railway

Trenitalia runs regional trains between Piedmont, Alpes-Maritimes and Liguria (Fossano (I) - Cuneo (I) - Tende (F) - Ventimiglia (I)). Due to Piedmont railway ineptitude from 2010 onwards, few trains runs along this route.

Other italian "international" services

• BLS runs trains between Brig (CH) and Domodossola (IT). Some come from Bern (CH), the Swiss capital. This is a somewhat fuzzy international service, because Domodossola is a border station (with customs), so the line is formally in Swiss, but there are 18 km and 3 stations in Italy before the actual border (and Piedmont region pays for Domodossola - Iselle service).
• Trenord runs S11 Milan suburban line between Chiasso (CH) and Milan (IT). However in Chiasso station there are "formally Italian tracks" S11 terminates on, so formally S11 trains never enter Swiss.
• Turin SFM line 3 runs till Modane (F), but again Modane has "formally Italian tracks".