Crisco will go off - it changes colour a little and develops an unpleasant flavour. At that point, I either throw it out or use it in something where the flavour won't be noticeable.
Flour bags do have a best before date on them. I don't stick to that strictly - I haven't had an issue with flour 6 months out of date, especially if it was unopened. But I can see it going stale if it is really old and/or open for a long time.
Granulated sugar shouldn't go bad unless it gets contaminated. Other sugars may become difficult to use due to clumping, like brown and icing (confectioners) sugar.
The test for eggs is to put them in a bowl of water. If they float, toss them. Or cook them up to feed to the animals, if you have dogs. If they stand upright but not out and out floating, they're on the older side. They should be fine for baking but if you are making your special omelette or quiche, I'd get new eggs. If they lay mostly horizontal, not floating, they're the freshest and will be fine for anything you want to do with them.
Baking soda and baking powder definitely lose their effectiveness the older they get. Once baking soda reaches the best before date on the box, use it for odour control in the fridge or cleaning but get a new box for baking. Baking powder is similar; I will use it past the best before date but I usually add a smidge more for a little extra oomph since it will have lost some. I believe the jar I have has a date line where you can write in when you opened it and the advice is to toss it once it's been open for 6 months.
Yeast is another one. I buy my yeast in bulk quantities. I only use it a couple of times a year but it still works out cheaper to toss some of it than it does to buy the smaller containers or packets. I store it in the fridge and will toss it every other year. Yeast can be checked, though. Just proof it before you add it to a recipe. If it doesn't proof? Try a second go round. If that one doesn't proof? Go buy new yeast. I take a coffee mug, warm the mug up with hot water, dump out the water, add in a tablespoon of granulated sugar and 1/3 cup of hot water, stir and sprinkle in a tablespoon of yeast. I'll stir the yeast in then put in a 100 F oven to rise. If your oven doesn't go that low, use a thermometer, heat it to about 120 F then turn it off but turn the oven light on. It will stay warm enough to let the yeast proof.