earth
If walking is your thing, you'll be spoilt here as there are pleny of oppotunities for the casual walker and the serious trekker. The "Chemin de St Jaques" is well known, but there are pleny of long and short "ballades" on offer to explore the "sucs", the plateau, the gorges and the mountains. To lazy to carry your pack? Then, hire a donkey and, like J.L. Stevenson, the Haute Loire is for you to explore. Take your bike along the klometres of "VTT" trails or go horse riding - All can be found in the Haute Loire. Even in winter there is plenty of reason to get out doors to ski, go walking in snow shoes, or even dog-sledding. If scaling heights or jumping into a void is lore your cup of tea there exist several sites for climbing and even bungie jumping...
Links to various sites offering services and information for the walker, climber, biker and the like, can be found here.
air
Hot air ballooning was all but born here and there is an international festival each year in the Autumn. If you want to expereince it yourself, there are "baptêmes" on offer at Chadrac and St Jeures. There are also opportunities for hang-gliding, paragliding and just plain flying!
water
With more than 3500 km of waterways and the beautiful gorges of the Loire and the Allier there are plenty of oppotunities to partake in a variety of watersports from "hot-dogging" to fly fishing. For the fishing enthusiast, a "carte" will cost 62€ for the year or 30€ for a fortnight; more information can be found here.
For the more active there are plenty of centres offering kayaking, canoeing and rafting etc. The Allier boasts more than 90km of navigable river and the Loire more than 100km. Links to a variety of centres can be found here. There are also "waterparks" at St Paulien and Vorey sur Arzon.