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As a physician, and someone who loves yogurt, I have looked into this quite carefully. I have explained what I have learned below - I hope that you will find it helpful.
Yes, it is perfectly safe to eat yogurt after the date stamped on the container, unless you notice signs of spoilage, such as a bluish-green tinge or a particularly sour smell or taste. This usually doesn't happen until quite some time after the date stamped on the container, so it is usually quite safe to consume yogurt for a good while after this date. In fact, this date is usually just a 'sell by' date indicating that the store must discard the product if not sold by that date. (This date is usually not a 'best before' date or 'expiry date' unless listed as such. If it is a 'best before' date, the product is again, usually quite safe to consume after the date, but it may taste a bit different - chips may taste a bit stale after this date, yogurt may taste a bit more sour after a 'best before' date. If it is an 'expiry date', you shouldn't really consume the product after that date - an expiry date is the date after which something in the product goes off, and is not as safe to consume.) However, this date is usually a 'sell by' date, as mentioned above, and yogurt most often lasts for some time after this date - usually for 2 to 3 weeks after this date.
Yogurt is made from milk which is pretreated to ensure that the only bacteria left in the yogurt are not harmful, and are simply 'good bacteria'. This helps to ensure that yogurt has quite a long shelf life, because harmful bacteria are not acting on the yogurt while it is waiting to be consumed. Also, yogurt is high in acidity, so this helps to extend the shelf life of the product. Yogurt usually lasts a good two to three weeks beyond the date on the package, unless you notice signs of spoilage which would indicate otherwise (such as an more than usual sour taste/smell, or a bluish-green tinge on the surface of the yogurt). You may notice some differences over time (if the yogurt is left in the refrigerator up to or shortly after the date on the container), but these are not signs of spoilage, or of anything that would cause you harm. Usually, the yogurt will develop some extra cracks in the surface over time, and it will develop a bit of extra yellowish liquid (the whey, or lactoserum) on the surface. Whey or lactoserum is harmless, and it actually contains a lot of the nutrients - most manufacturers note that if this is present, it should be stirred into the yogurt before consuming it, to ensure that you get the full nutritional value from the product. (I don't do this - I prefer to pour off the whey, and then, if
needed, I just whisk in some extra cold water to adjust the texture.) Commercial yogurt doesn't develop this lactoserum right away, because it is treated to prevent the bacteria within the yogurt from forming any whey or lactoserum. (Homemade yogurt, which is not treated in this way, tends to develop whey or lactoserum quite rapidly, within a few days of preparation, and this too is just natural, and not at all harmful.) consumed. (However, if you do consume yogurt with this sour taste/smell or even yogurt with a bluish-tinge (indicating mold formation), the worst that will happen is a slight tummy-ache and perhaps some diarrhexa, and these are self-limiting, and resolve harmlessly without any sequelae, usually within 12 to 24 hours.
The date on yogurt, and on most food products, is a 'sell by' date unless otherwise specified. This is a date after which the store must remove the product from the shelves - but the product is not spoiled, and can still be consumed safely for quite some time after that date. If the date is listed as a 'best before' date, then the product may change slightly in colour, texture or taste, but it is usually still able to be consumed safely for a while past that date. For example, chips may taste a bit stale after the best before date, but they are still safe for consumption. If the date on the product is an 'expiry date', then the product should not be consumed after that date - an 'expiry date' indicates that after that specified time, some component(s) of the product becomes unsafe for consumption.
At any rate, yogurt is a product with a long shelf life which can usually be very safely consumed for around 2 weeks after the date listed on the package, which is usually a 'sell by' date unless otherwise noted. It may change slightly in that there may be some whey or lactoserum on top of the yogurt, and the yogurt may have some surface cracks. These changes do not indicate any harm at all - in fact, most of the nutrients in the yogurt are in the lactoserum / whey, so it is often recommended that this liquid be stirred into the yogurt prior to consumption. The product is not safe for consumption if a particularly sour taste or smell, or a bluish-green tinge, are noted. If this is the case, the yogurt has gone off. The sour taste or smell is produced by the 'good bacteria' which live in the yogurt - it is a result of the byproducts of bacterial action on the yogurt, and it can be noted after the bacteria have had some time to act on the yogurt. The bluish-green tinge is an indicator that mold has begun to grow on or in the yogurt. Consumption of 'bad yogurt' though, usually does not result in serious consequences - mild diarrhea and nausea (a 'bad tummy') may occur, but these symptoms are most often self-limiting and should subside in 12 to 24 hours.