The following is not necessarily an exhaustive list.  If anyone knows other models that feature MGRS capability, please click HERE to eMail Joe Mehaffey the information.

You may have to load the latest firmware in some models to have MGRS capability.

Garmin

Geko 101, 201, 301
Foretrex 101 and 201
eTrex Vista Color and Legend Color
The entire GPS 60 family
GPS 76C and 76CS
GPS 72
iQue 3200 and 3600
GPS 276 and 296
GPS 96 and 96C
Quest
eMap
GPS II+
GPS III+
GPS 12 Map
GPS 12, 12XL, 12CX
GPS 76, GPSMAP 76, 76S, 76C, and 76CS
GPSMAP 176, 176C
All eTrex series units
GPS V
GPS III Pilot
GPSMAP 295 
Rino (all)

Lowrance
iFinder
 

Magellan
M315, M320
M330, M330M
Meridian Basic 
Meridian Color
Meridian Gold
Meridian Platinum
Meridian Marine
SporTrak Pro
SporTrak Map
SporTrak
SporTrak Color

MGRS and Lon/Lat simultaneous display. 
The following units offer the option of displaying MGRS and Lon/Lat coordinates simultaneously.  This is useful for military use.  Ground troops use MGRS and air support uses Lon/Lat. 

GARMIN
eTrex Legend and Vista
The entire GPS-60 family
GPS-76, map76, map76S, 76C and 76CS
Foretrex 101, and 201
Geko 101, 201, 301
Quest
Rino 110, 120, 130

MAGELLAN
With the latest firmware updates the following units also provide simultaneous MGRS-Lat/Lon display

Magellan SporTrak series
Magellan Meridian series

To get to the simultaneous display:  toggle left or right at the single position display.

(The following is by courtesy of Frank Rossi)
NOTE:  MGRS, USNG and UTM:  the "easting" is always before the "northing".

However in Latitude and Longitude:
The Latitude is always listed before the Longitude.
Probably from the old celestial navigation days when Latitude was much more
accurate than Longitude.  It took the development of the chronometer for
accurate time to have accurate Longitude.
Therefore you should use "Lat/Lon".

USNG (US National Grid) is essentially identical to MGRS in the US.
USNG (NAD83)
MGRS (WGS84)