Ewan
Don't know if you are thinking of visiting SE Asia, but for caving in Laos, Vietnam and Sarawak you will need official permission and this can take months to obtain. Sometimes these permits can be obtained by local tour companies. Also avoid May to November (rainy season).
Some suggestions for good sport trips in Thailand and Laos are
Thailand:-
Tham Mae Lana, Mae Hong Son - 9 km river passage - through trip
Tham Nam Lang, Mae Hong Son - 8 km river passage
Tham Phra Wang Daeng, Phitsanulok - 10 km river passage.
Tham Pha Phueng, Nan - deepest cave in Thailand with a 127m pitch
Doi Ang Khang area, Chiang Mai - several caves explored to 250-300m deep
Laos:-
Tham Xe Bang Fai, Khammouane - huge river passage, through trip, BIG spiders
Tham Nam Xang Nua-Tham Houey Leng, Vientiane - 300m deep, 3.5 km long through trip
The 'Atlas of Great Caves and Karst of Southeast Asia' by Laumanns and Price, published by Berliner Hohlenkundliche in 2010, is the best source of information on caves in this region.
Martin