83 apps at the moment... have had as many as 113... no clue if there is a performance breaking point.

 

I had 114 apps on my Rezound and have/had pretty much the same apps on my RAZR MAXX, Note II, and LG Spectrum. The number of apps doesn't seem to effect performance. Most apps just sit there dormant in storage memory.

The Android OS runs copies of app after app in active memory until active memory gets full. Then when the OS needs to run another app it automatically knocks a little used app(s) out of active memory to make space.

 

155 and no problems

Edit: that is 155 from the Google play store.
Throw in another 1/2 dozen or so from side loading and/or Amazon app store and/or pre-loaded.

 

About 35 (From the Play Store) on my current handset, I have had as many as 130 in the past, never seems to affect performance.