Hungary's capital boasts the first subway on the European continent. Line 1 (also known as 'Földalatti' or the Millennium Underground) was built in 1896 and added to Budapest's UNESCO World Heritage entry in 2002 [unesco.org]. Old stations have been beautifully restored and some of the modern stations on the other lines are also worth a look.
Millennium Underground Museum. Exhibition about metro construction, its achievements, and future. Since 1975. Location: A disused tunnel section in the Deák Ferenc tér metro station. Address: Budapest, Deák tér, metro station. Hours (check before visiting): From 10:00 to 17:00 daily - except Mondays. Admission: 270 Ft. Reference: bkv.hu (official website).
Urban Public Transport Museum Szentendre. About Budapest public transport including the suburban railway. Since 1992. Address: 2000 Szentendre, Dózsa György út (in a suburb of Budapest). In front of Volán bus station, to the left. At Szentendre suburban metro station. Hours (check before visiting): From April to October between 10:00 and 17:00 daily, except Mondays. Admission: 270 Ft. Reference: bkv.hu (official website).
"[Dong-ding] Tessek vigyazni, az ajtok zarodnak" ("Please be careful, the doors are closing"), pre-recorded male voice (mp3 from metrobudapest.fw.hu). In refurbished trains there's a female voice: "[Dong-ding] Kerem vigyazzanak, az ajtok zarodnak" (meaning the same, mp3 from freeweb.hu).