What components of the Boeing 787 are made out of titanium?
The Boeing 787 is special due to its high count of composite parts. When aluminium comes in contact with graphite fiber, contact corrosion will damage the aluminium whereas titanium will be unaffected due to its higher position in the electrochemical series.

15% of the initial 787s empty weight consists of titanium, a fraction much higher than in other airliners and one of the reasons that Boeing lost 23 million USD on each of their 787s sold initially.



787 material breakdown (picture source). Dark grey is carbon fiber composites and light grey is glassfiber composites.

The linked Reuters article contains a few parts which Boeing made from titanium in the first 787s:


  Boeing has changed the cockpit window frame to aluminum from titanium, and has changed the frames of some doors to composite from titanium. Special coatings or materials are used to prevent aluminum corrosion, experts said. It wasn’t known how much Boeing saved by the change. Boeing declined to comment.


The article goes on to mention a part in the wing-fuselage connection which is milled from a solid block of titanium. 97.5% of the block is lost when it is machined - very similar to the Tornado center wing box! 

Another use of titanium is in the hi-lok fasteners which are used to bolt metallic or graphite parts together. I would expect that those are the biggest use of titanium in regular aluminium airliners, because using titanium hi-loks instead of steel results in weight savings.