It surprises me how many people consider diarrhea a dire emergency. A pet can be coughing for weeks and I never see them, but they have diarrhea on the owner's floor one time and they're right in. Most of the time these are cases that would resolve on their own, and there isn't really a need to see the vet. However, there are some guidelines to follow, as diarrhea can also indicate some health problems that should be addressed.
If your pet has diarrhea for 1-2 days but is otherwise acting normal and eating, it probably doesn't need to be seen. If there is vomiting at the same time and the pet isn't eating, I would definitely recommend a vet visit. If the diarrhea continues for 3 days or more, you should see the vet, even if it turns out to be minor.
Most people are highly concerned about dehydration when their pet is vomiting or having diarrhea. Honestly, dehydration doesn't happen that quickly in most cases. Unless the symptoms are severe, a pet isn't going to easily dehydrate from a little diarrhea.
Another concern is if there is blood in the stool. This really freaks people out, even though it's usually minor. Most commonly this is small drops or streaks of blood in the feces or some small clots of blood. Even though the sight of blood panics people it's not always a cause for concern. When the colon is irritated, the lining might bleed a little bit. This is merely a sign of irritation (colitis) and usually not a serious problem. However, if the blood is profuse or if there is any bleeding from anywhere else, it can indicated more serious problems.
So keep this in mind the next time your pet has a little loose stool. You may be okay to wait it out for a few days rather than rushing right to the vet.