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
The objective of this study was to determine whether workers exposed to titanium dioxide (TiO2) had significantly higher risks of lung cancer, chronic respiratory disease, pleural thickening/plaques, or pulmonary fibrosis than referent groups.
A total of 1,576 employees exposed to TiO2 were observed from 1956 through 1985 for cancer and chronic respiratory disease incidence, and from 1935 through 1983 for mortality. A cross-sectional sample of 398 employees was evaluated for chest roentgenogram abnormalities.
Cohort analyses suggested that the risks of developing lung cancer and other fatal respiratory diseases were no higher for TiO2-exposed employees than for the referent groups. Nested case-control analyses found no statistically significant associations between TiO2 exposure and risk of lung cancer, chronic respiratory disease, and chest roentgenogram abnormalities. No cases of pulmonary fibrosis were observed among TiO2exposed employees.
(C)1988 The American College of Occupational and Environmental Medicine
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.