Main attraction of the largest of the Canary Islands is El Teide, the still fuming (albeit very little) volcano. This mountain is Spain's highest, reaching up 3718 m. The climb is easy but restrictions apply to control the influx of tourists, who can easily reach the summit by cable car.
Much less frequented is the impressive Pico Viejo, the old volcano, adjacent to El Teide. This volcano complex is situated in the centre of a huge caldera, a colourful plain at height of 2000 m, formed by an ancient explosion, a beautiful surrounding for moon-like walks.
Tenerife has much more to offer to the hiker. There are ravines, mountain massifs, lunar landscapes, canals for easy level hiking, a lush green north coast, subtropical vegetation. The infrastructure of the island is good, helping you to reach your hiking destinations and finding a place to sleep. Maps and guides are available in many languages.
Apart from the GR131, the main trail of Tenerife, the island has a pilgrimage way: the Camino de Santiago de Tenerife, connecting Puerto Santiago on the west coast to Santa Cruz de Tenerife from where many ferries depart. Many more local trails explore the island, often climbing and descending a lot.
Check the complete list of Canary Islands.