Well known Trekking-Tours in Bhutan:
 
Name                                 Start                       End            Duration      max.Elevat.     open

1 Bumthang Cultural Trail     Jakar                       Mesithang    3 days        3.360m          March-May / Sept.-Nov.
2 Druk Path                        Thimphu                                      6 days        4.200m          Feb.-June / Sept.-Dec.
3 Jomolhari Trail                  Thimphu (Dodera)                         8 days        5.000m          May-Oct. (best: end of Sept.)
4 Laya - Gasa                     Tashithang (Punakha)                 14 days        5.000m          Apr.-June / Sept.-Nov.
5 Snowman                         Paro or Punakha                        25 days        5.300m          Sept./Oct.

Trekking:
High altitude climbing above 6.000m is long forbidden in Bhutan. The peace at the mountains as resting places of Gods must not be disturbed. Therefore no infrastructure for such extreme altitude endeavours exists. 
For highland trekking there are a number of possibilities, most of them start and end either in Paro, Thimphu or Bumthang. The trak-routes are moving over high plains, snowfields, mountain ridges and are passing tiny villages.
For detailed descriptions we recommend Lonely Planet Guide Bhutan (ISBN 1-86450-145-8, www.lonelyplanet.com). Suitable for planning is also the "Trekking Map Bhutan" 1:390.000 from Himalayan Maphouse (GPO Box 3924, Kathmandu, Nepal, Fax +977-1-228 340, e-mail: maphouse@wlink.com.np, Internet: www.himalayan-maphouse.com).
In spring time the Rhododendrons are flowering and in autumn you have good chances for far reaching views and clear skies.

Be aware, you are moving mostly between 2.500 and 4.000m altitude with almost no civilisation and settlements, you have to bring your own infrastructure.
In case of accidents or illness rescue operations need quite a time, so take with you a well stocked pharmacy and as a priciple: don't take risks or go at all if your physical constitution may not be up to it.
A new 3 day tour, the  "Bumthang Owl Trek"  starts at Menchugang and leads via Dhur and the Drangela pass to Jakar.
A special description of this new route you will find - here.