All mentioned hours are without rest! As the Karwendel has many possible entries/exists the tours can be adjusted at will. From the five selected tours it is clear the Karwendel is there for everybody.

Tour 1
-Childrens (8-12)/ Pensioners tour

Take it easy tour. Times given are for adult walkers, multiply by an estimated factor for personal times. 
Starting point: Innsbruck
day 1: Ascend with cable-railway to Seegrubbe or Haflekar -
       walk to Pfeishutte
       3-4hrs
day 2: Pfeishutte - Mosalm
       2-3hrs
day 3: Mosalm - Scharnitz (make reservations!)
       3-4hrs
day 4: Scharnitz - Karwendelhaus
       4-5hrs 
day 5: Karwendelhaus - Falkenhutte
       2-3hrs
day 6: Falkenhutte - Lamsjochhutte
       4-5hrs
day 7: Lamsjochhutte - Schwaz - Innsbruck (by train)
       3-4hrs

Tour 2
-Hikers tour

Just one of the many possible tours for hikers. When time is available some extra days can be taken to climb peaks 
Starting point: Schwaz
day 1: Schwaz - Lamsjoch hutte
       4-5hrs
day 2: Lamsjoch hutte - Karwendelhaus, skip Falkenhutte
       6-7hrs
day 3: Karwendelhaus - Hallerangerhaus, via Birkar spitze
       7-9hrs
day 4: Hallerangerhaus - Pfeishutte
       3-4hrs
day 5: Pfeishutte - Solsteinhaus
       6-8hrs
day 6: Solsteinhaus - Nordlinger hutte
       4-5hrs
day 7: Descend to either Reith or Seefeld 
       2-3hrs

Tour 3
-Powertour

If you want to show you are tough, try this 
Starting point: Kranebitten
day 1: Kranebitten - Solsteinhaus, skip N. Magdenburger hutte.
       4-6hrs
Day 2: Solsteinhaus - Karwendelhaus, take the high road 
       via Zirmalm, descend to Angelre and do the    
       Geierschbachklamm. Great and mostly lonely (at first)! 
       10-12hrs
day 3: Karwendelhaus - Lamsjochhutte, skip the Falkenhutte.
       6-8hrs
day 4: Lamsjochhutte - Hallerangerhaus, do not climb
       Lamsenspitze! No time for that. Long but great.
       10-12hrs
day 5: Hallerangerhaus - Seegrubbe berghotel, skip Pfeishutte
       (make reservations in the hotel)
       7-8hrs
day 6: Seegrube - Neue Magdenburger hutte, via Kemacher 
       and frau Hitt
       5-7hrs
day 7: Neue Magdenburgerhutte - Nordlinger hutte skip 
       Solsteinhaus
       7-9hrs
day 8: Nordlinger hutte - Scharnitz
       4-5hrs

Tour 4
-Gipfelsturmers tour

For those who cannot stand something above them 
Starting point: Schwaz
day 1: Schwaz - Lamsjochhutte, climb Lamsenspitze
       6-8hrs
day 2: Lamsjochhutte - Falkenhutte, via Hahnkampl spitze 
       and optionally Sonnjoch. 
       5-9hrs
day 3: Falkenhutte - Mahnkopf - Steinfalk - return to 
       Falkenhutte - Karwendelhaus
       6-7hrs
day 4: Karwendel hohen tour: Karwendelhaus - Birkarspitze - 
       Odkarspitzen - Marxenkarspitze - Breitgriesskarspitze - 
       Pleisenhutte. Only for experienced and steady walkers!
       Don't try in spring when there is still snow!
       9-11hrs
day 5: Pleisenhutte - Solsteinhaus, in afternoon climb 
       Erlspitze
       6-8hrs
day 6: Solsteinhaus - kl and gr Solstein - Neue Magdenden
       burger hutte
       4-6hrs
day 7: Neue Magdenburger hutte - Hohe Warte - Vord Brandjoch
       (descend from Hohe Warte first!) - Frau Hitt - 
       Kemacher - Haflekarspitze - Seegrube Berghotel
       6-8hrs
day 8: Seegrube - Mannspitze - Rumerspitze (II!) - Pfeishutte
       5-7hrs
day 9: Pfeishutte - Thaurerjoch spitze - Stempeljoch spitze -
       Speckarspitze - Betelwurfhutte
       6-8hrs
day 10:Betelwurfhutte - kl (III!) and gr (I) Betelwurf 
       - Schwaz 
       6-8hrs

Tour 5
-Roundtrip Karwendel

When you want to see it all (well, almost) 
Starting point Schwaz
day 1: Schwaz - Lamsjochhutte, climb Lamsenspitze
       6-8hrs
day 2: Lamsjochhutte - Falkenhutte, via Hahnkampl 
       4-6hrs
day 3: Falkenhutte - Tolzerhutte
       Depending on the road taken 7-10hrs.
day 4: Tolzer hutte - Karwendelhaus
       7-8hrs
day 5: Karwendelhaus - Krinner Kofler hutte
       5-7hrs (careful on the gjaidsteig when it rains!)
day 6: Krinner Kofler hutte - hochland hutte -
       Mittennwalder hutte
       6-8hrs (One can also stay in the hochland hutte)
day 7: Mittenwalder hutte - Brunsteinhutte
       depends on the selected road: 3-7hrs
day 8: Brunsteinhutte - Brunnensteinspitze - 
       Hallerangerhaus
       8-9hrs
day 9: Daytrip to Betelwurfhutte, and/or climb a peak at 
       will
       min 3hrs
day 10:Hallerangerhaus - Pfeishutte (do the pleisenspitze
       and thaurer joch spitze if desired)
       min 4hrs
day 11:Pfeishutte - Solsteinhaus
       6-8hrs
day 12:daytrip Neue Magedenburger hutte and/or climb 
       peaks at will. Do not under-estimate the 
       schutzsteig, you will need your hands
       min 3hrs
day 13:Solsteinhaus - Nordlinger hutte
       5-7hrs
day 14:Nordlinger hutte - Reith - Innsbruck - Hafelekar
       round-trip at desire on the Innsbucker nordkette.
       2-3hrs to get to Reith.

Tour 6

-The monkey tour

If you like to use your hands. Be carefull with the weather and verify the conditions of the tracks with the keepers of the cabins. Most tours have lower alternatives. 
starting point: Hotel Seegrube (Innsbruck)
day 1: Hotel Seegrube -> Solsteinhaus, via Innsbrucker klettersteig
       and gipfelsturmers weg
       6-8 hours
day 2: Solsteinhaus -> Nordlinger hutte, via Freiungen hoheweg
       5-7 hours
day 3: Nordlinger hutte -> Brunnsteinhutte, via Epzirl-alm,
       Scharnitz
       7-9 hours
day 4: Brunnsteinhutte -> Hochland hutte, via Brunnsteinspitze
       and Mittenwalder hoheweg. Descend via Pfredigstuhl is
tricky!
       7-9 hours
day 5: Hochland hutte -> Karwendelhaus, via Gjaidsteig
       5-7 hours
day 6: Karwendelhaus -> Hallerangerhaus, via Birkarspitze
       8-10 hours
day 7: Hallerangerhaus -> Innsbruck, via Betelwurfhutte, climb 
       Grosser Betelwurf(I) without backpack and descend to 
       Absam. The bus to Innsbruck you can find the first street
       left when you leave the Halltal.
       8-10 hours