Ride 'quailty' very much depends on the tubing profiles. Steel, aluminium and titanium can all be built into very stiff frames, or very flexy frames.
Titanium is denser than aluminium, but not as dense as steel. Oversizing a tube, say increasing the diameter by a factor of two but keeping the wall thicknesses the same increases the stiffness of the tube by a factor of eight. Go too far though and the tubes can buckle. So light materials can be oversized to increase stiffness but at little weight penalty. This allows titanium to build into lighter frames than steel, yet still retain a decent stiffness (very light steel frames tend to flex a lot!).
Titanium is also corrosion proof. Both steel and ti have a fatigue limit, ie you can flex them an infinite amount of times below a certain level and they will not fatigue. Alu does has no limit, which is why we tend to see them built stiffer to increase durability. However, as above, is a light material, and oversizing can be taken advantage of so the frames still end up light.
Titanium also elongates much more than steel or alu when under load. This makes the material tough and able to cope with impacts.
So why do peole like titanium? The ride quality is a myth - as above, so much depends on how is designed. But it is resilient, corrosion proof, builds into lighter frames than steel for the same stiffness, great fatigue qualities and as doesn't need proofing, further weight saving can be had.