In digital electronics (with HIGH/LOW logic signals) resistors are usually only used as a pulldown or pullup, in order to define a default state of LOW or HIGH respectively.
In analog electronics resistors are all over the place with many uses, for instance current-limiting for an LED is a case of this.
Another analog use is when two resistors form a voltage-divider, allowing the ADC to read a voltage higher than the Arduino's supply voltage safely.
With any new sensor or chip the thing to do is read the datasheet, perhaps jumping to the "typical application" circuit to get an example of its use - this will often answer the question "do I need some resistors/capacitors with this".
When a sensor or chip comes on a module often this has already been done for you (though not always), making life a bit simpler.