Kenmore is made by different manufacturers and they all just put the Kenmore name on it. Like any other major appliance purchase; if you can get it from a reputable store (Sears, Home Depot, etc.) you've got the store standing behind that purchase. I personally tend toward Kenmore appliances.
My conditioning fridge, however, is a Frigidaire upright (with no freezer compartment) that came from Sears and so far it is the only major appliance I've had a problem with, and Sears came back out within 2 days with a replacement (this was within 2 weeks of purchase). No problems since.
My fermeezer is a Kenmore chest unit (Sears) and has been plugging away faithfully for over a year now with nary a problem. The rest of my house (basement freezer, entire kitchen, etc.) is all Kenmore and thus far (several years) I've had no problems.