Limited Express Hamakaze (はまかぜ) connects Osaka (大阪) with Tottori (鳥取) Kasumi (香住) and Hamasaka (浜坂). Even though there is only one round trip, Hakamaze is only train that connects Osaka with Tottori directly by Japan Rail Pass or other JR rail passes without any extra charge. Actually the primary train goes to Tottori from Osaka is Limited Express Super Hakuto. This train is much more frequent and much faster than Hamakaze. But this train goes through Non JR line, Chizu Kyuko Railway. Therefore you have to pay extra charge if you want to take this train by Japan Rail Pass or other JR passes. Please check the post, The fastest access to Tottori from Osaka, Shin-Osaka and Kyoto, Limited Express Super Hakuto to get the details.
Hashidate connects Kyoto and Miyazu, Amanohashidate and Toyooka. This is only train to go directly one of “Three Views of Japan”, Amanohashidate.
This train, Hashidate goes through KTR (Kyoto Tango Railway) between Fukuchiyama and Toyooka. So if you use this train and go to stations further than Fukuchiyama by Japan Rail Pass, you have to pay extra fare. But if you use Kansai Wide Area Pass, Kansai Hiroshima Area Pass or Kansai Hokuriku Area Pass, this segment on KTR is covered.
Kinosaki (きのさき) connects Kyoto (京都) with Kinosaki-Onsen (城崎温泉), Toyooka (豊岡) and Fukuchiyama (福知山). When you go to the popular hot springs town, Kinosaki or one of “Three Views of Japan”, Amanohashidate (天橋立) from Kyoto you may take this train.
Maizuru (まいづる) connects Kyoto with Maizuru (舞鶴). This limited express train is always combined operation with Kinosaki between Kyoto and Ayabe (綾部).
Konotori connects Shin-Osaka (新大阪) and Osaka (大阪) with Kinosaki-Onsen (城崎温泉), Toyooka (豊岡) and Fukuchiyama (福知山). When you go to the popular hot springs town, Kinosaki or one of “Three Views of Japan”, Amanohashidate from Osaka, you may take this train.