Could neutralisation of safe chemicals produce dangerous ones? I'm basically thinking whether I could potentionally poison myself while neutralising strong acid/base by some weak base/acid when I accidentally spill it, touch it or when I'm cleaning reaction product.

Combinations of chemicals that are non-toxic in my opinion:


$\ce{HCl + NaHCO3}$  
$\ce{H2SO4 + NaHCO3}$
$\ce{NaOH + CH3COOH}$


None of these are poisonous. I just thought these up, for example the first one produces table salt, $\ce{NaCl}$.  

But could there be a combination of non-toxic acid and base that would produce some nasty salt when neutralised? Something worse than what I would be getting rid of?
Is there a combination where I should better just wash myself with water?
While not an acid-base reaction, an example of mixing two relatively "safe" chemicals to form dangerous ones is bleach (sodium hypochlorite) plus ammonia - both common household chemicals. This reaction yields chloramine, dichloramine, and nitrogen trichloride, all more toxic and hazardous than bleach or ammonia.