I haven't been able to find much in regards to titanium cookware and its possible interactions with the human body.
Please provide academic/peer-reviewed/scientific articles if possible.
You cannot view the full study, but the summary already tells you the results: http://journals.lww.com/joem/Abstract/1988/12000/Epidemiologic_Study_of_Workers_Exposed_to_Titanium.11.aspx
Note: Titanium always has a TiO2 layer above it, which is why your food won't get into contact with titanium directly (and if it does, it'll quickly oxidize to TiO2 again).
The result of that study is consistent with the fact that titanium is widely used for medical purposes like implants and dental fillings. Even pacemakers are made from titanium. It is not toxic, even in high doses and on permanent exposure (the medical "lifetime" of the titanium is somewhere along the lines of 20 to 30 years, without a single toxic effect ever linked to the titanium).
The only thing that is hazardous is titanium nano-particles. But the nano-particles of pretty much any element, including carbon, will be hazardous, so that doesn't count (it's not chemically toxic, the physical size is what makes it dangerous). You won't ever be exposed to nano-particles from using titanium cookware, so to answer your question: Yes, titanium cookware is completely safe. There are no cases of allergies recorded (at least I didn't find any) nor is it toxic.