Doug, Over 120 years of experience in the field has proven the traditional .38-55 load (255 grains at 1320 fps) is effective on Class 2 game (deer, black bear and similar size animals) within its maximum point blank range (+/- 3 inches) of about 135 yards. ------- Details below : chuckhawks.com/38-55_gentle_medium.html

My grandfather used one and found it adequate but as soon as the 35 remington was available in the Marlin 336 he bought one.

The Balistics for this round seem good for hunting
Ballistics and Drop for the .38-55 Winchester
.38-55-winchester
Cartridge Type: Rifle
Height: 2.085"
Width: 0.506"
Average FPS: 1320
Average Energy: 986
Average Gr: 255
Recoil: 1.51
And an effective range of 350 yards
http://gundata.org/cartridge/98/.38-55-winchester/

I have not personally, I have used mostly a 30-30 or a 30.06, The .38-55 is used to hunt black bear and deer at moderate ranges and is also used in cowboy action shooting side matches.
And there are several videos on youtube of people taking deer with this cartridge