I've gone through lots of office chairs in my house; I use them for all of my household chairs and usually get them on the cheap. The most common failure modes from memory:

1. caster breaks
2. seat breaks off of the post
3. raising/lowering mechanism malfunctions, usually causing it to be permanently lowered or uncontrollable
4. wherever the back rest attaches to the rest of the chair breaks off - if there is an arm, then this happens on the bottom of the arm
5. bottom of the post breaks through the frame for the casters - even if still functional, it now scrapes the floor
6. fart smell

On all-steel frame, fairly solid chairs I've only ever seen the post break once and otherwise it was always casters snapping off at the connection. But those are not only expensive but very heavy, and tend to be less adjustable.