Which situations would cause a company to ground or recall a aircraft series?
There are various levels that a grounding can occur at. 


Governing Agency: A legal authority can ground an aircraft make/model/serial number range (or one containing a certain part/system) if it deems they are unsafe or there is some question about the airworthiness. The most recent example of this was the recent grounding of the 787's by the FAA after the battery issue was called into question. Governing agencies can also practically ground an aircraft/make/model by issuing a mandatory AD against it; this will practically ground all airframes until proper maintenance occurs. A federal entity may also chose to not certify an aircraft for operations within a country, and/or the manufacturer may chose to not seek certification in that country although some countries allow one off certificates to be issued. In emergency situations the local governing body may shut down and ground all aircrafts in a certain area. The most prominent example of this that I know of is when all aircraft were grounded following the 9/11 attacks; this is generally more of a ground safety issue than an airworthiness issue.
Operator: The owner/operator can ground an aircraft for safety reasons if they belive there may be an issue with the functionality or operation of the aircraft in question. A good example of this is the grounding of the Southwest 737 fleet due to weight and balance issue, this was done by the airline potentially before a governing authority intervened. Another example was ANA's grounding of its 787 fleet due to engine problems. 
Pilot In Command: As the pilot in command of a flight and the one responsible for ensuring the safety of the flight you can ground an aircraft for any reason you so chose and be well within your rights. Let's say on your preflight checks something is out of place or looks wrong; in such a case, the pilot can ground the aircraft until the issue is fixed. 
Maintenance Persons: Generally when attacked from this angle it's more of a prevention to return to service than a grounding, but if an issue is found during a stage check or annual the aircraft may be pulled until the issue is fixed. There is an interesting article about withholding maintenance signatures here.
Recall: Manufacturers generally provide AD's instead of a full blown recall however some cases may warrant a full blown recall of airframes. When Porsche dropped the TC for the PFM3200 engine Mooney offered a recall of sorts, the owners could either sell the aircraft outright or the engine retrofit would be subsidized.