While I agree with warren's answer, I do believe like Ray points out that this is mostly about the original sin, transmitted from Adam to all of his offspring.
Total depravity goes beyond that, as it states that we are not only sinners, but that we are not even righteous enough to accept Christ on our own (keep in mind this doctrine was formulated as an answer to Arminianism, which pretended that men had enough good in them to accept Christ).
On the fact that all have sinned, we can refer to Romans 3:23:
For all have sinned, and come short of the glory of God;
and on the fact that we are not able to deserve salvation by our own efforts (which is somehow what Arminianism implies), you can see Titus 3:5:
Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;