I'm not sure there is a limit of number of dataframes. I would suppose it would be left up to the user to decide how many would be useful. ArcGIS Help 10.1
Thanks for reply, but it would be great if you could inform me what is the maximum number?
Are you worried about performance, or are you just wanting to know the theoretical maximum? If I were a betting man, I would guess 2,147,483,647
http://resources.arcgis.com/en/help/arcobjects-net/componenthelp/index.html#//001200000980000000
Looks like the IMaps2.Count is an integer, so that value should be accurate. You aren't planning on adding more than that, are you? Hah!
No problem - I think it's safe to say you should be able to add as many as you'd like for a legitimate mapping need, with performance as the wildcard - that's why I mentioned the theoretical maximum vs. reality (performance impact/memory limitations on your machine, etc.). Giving an exact amount for the later wouldn't be possible, I do not believe, as it's very nebulous...
The data you load, what you are doing within the data frames, how much memory your machine has, etc. - there are many parameters that would come into play. But, like for map layers, the physical, theoretical limitation in the Esri code should be 2,147,483,647 - this is the maximum number an integer type supports. All other things aside, this should be your absolute max!