I cancelled my service with Sprint, knowing there would be a $150
cancellation fee.  When I recieved the final bill, there was almost
$25 in taxes based on the $150 fee.  Is it legal to charge taxes on
fees?

Taxes are charged by the government, not the phone company.  Sprint
(along with other retailers and service providers) is merely
responsible for collecting government-imposed taxes.  This is not a
question of legality, so much as it is whether they charged you in
error.  You may wish to contact the level of government (city, state,
fed.) to whom the taxes are supposed to go to confirm.

Spring also has a new fee to upgrade your phone - and taxes on those fees also.

Many of the taxes are actually just additional fees that sprint
charges - probably all covered by you user agreement.....