Patch or replace tube? Is it worth patching a tube on a mountain bike, or just replace it with a new one? 

There are a lot of 1/2" - 3/4" thorns here in Texas, and I use 26 x 1.95 tubes. 

Any particular patch type/brand is better? Can you recommend any methods to cut down on punctures?
I think that it is definitely worthwhile to patch a tube for many reasons:


five patches go for about $5, lower than the price of a single tube (~$7). 
a patch kit can be taped under the seat whereas a tube must be carried in a bag or pocket (and if in a pocket, remembered).
Given the ability to avoid flats almost entirely (e.g. using puncture-resistant tires, riding mindfully / carefully), I have never had to wait for a patch to 'dry', even the minute or two for the glue to set passes pretty quickly. Except when in a rush (e.g. a mountain bike race), it takes this much time to change a tube.
Tubes deteriorate more quickly and are more likely not to work when needed than a patch. For example, improperly folded tubes often crack where folded or at the base of the stem. 


Despite my own advice, in practice I carry a spare tube in my pocket if one is handy.

On a side note, if you have neither a tube nor a patch kit you can


tie a knot in the tire where the hole is and stretch
ride home on a flat and risk damaging your rim
stuff the tire with grass or something else handy
hitch hike
call a friend/ family member