Contra: 110 to 120 bpm - generally most dances will be in this range but the occasional contra at 105-109 can be good as a change of pace, and bands will occasionally hit 125. Some callers make the mistake of getting the band to play below 110 for the first dance to give beginners more time for the moves. But it takes skill to dance slowly; it is much better, for the beginners, to play at standard speeds.
Country Dancing: 90 to 120 bpm - in the first half of the 20th century speeds up to 135 were normal, but things have slowed down. Some dances work well at below 100, but historically lower speeds were an opportunity to put in more footwork rather than just to walk more slowly. Occasionally you will get one much slower, as low as 80 bpm. Likewise a dance like "Monica's Delight" is usually danced at well over 130 bpm.
Appalachian Big Set/Running Set: 120 to 140 bpm!
Waltz-time dances: around 120 to 140 bpm - some dances work well to slightly slower music but it can become a little laboured; faster than 150 can be tiring, although some traditional dancers dance the couple waltz to much higher speeds.
Hornpipe-step dances: 80-90 bpm (not to be confused with hornpipe tunes, these are dances with a strong step-hop, like Nottingham Swing and Clopton Bridge).
It is important to judge the situation when choosing a tempo. The best tempo will depend on the dance, the state of the dancers, whereabouts in the programme you are and lots more.