What is the bandwidth of human speech?
That really depends on your requirements and on your exact definition of bandwidth. 

Telephone range (300 Hz-3.4 kHz) has okay intelligibility but the quality of the voice is fairly compromised. For example it's hard to tell the difference between "s" and "f" sounds.  

80 Hz to 8 kHz gives you very good quality, although it's still possible for the human voice to make sounds outside of this range. Someone like James Earl Jones can easily go don to 50 Hz and specially trained singers can go a lot lower. Some fun examples at https://www.youtube.com/watch?v=lkdMl1ITw5M

If you want all of it, you should go for the range of hearing which is about 20 Hz to 20 kHz.