What good substitutes for saffron exist?

As for flavor, there really isn't a substitute.

Infusing saffron strands in a warm acidic liquid such as white wine will help extract the maximum flavor.

Whole saffron while more expensive than ground is a better use of your money as you know you're getting only saffron. Ground saffron, while not usually found in stores in the U.S. may be sold by mail order or overseas and is usually less expensive because it's being cut and blended with other spices such as turmeric but won't have the same flavor.

While this isn't a substitute, you can get better deals on saffron and make it go further.

First of all, do not buy it at a normal grocery store. It tends to be very expensive there. Instead go to a farmer's market (not one that happens every Thurs evening at the local church, but rather the big store). I'd imagine most major cities will have one or more. Atlanta has at least 4. Saffron is much, much cheaper at the farmer's market.

Second, thoroughly grind the saffron before using it. This will help the saffron more completely flavor a dish, requiring a smaller amount of saffron to get the flavor.

A quick Google suggested Tumeric, but I can't really imagine that working, nor did a lot of the comments on the internets.

The simple answer? None.

If you want to get the reproduce the color of saffron you can use annatto or turmeric. These will change the flavor of your dish though.

There is no replacement for the flavor of saffron. This is one of the contributing factors to it's high price.

This isn't an ideal solution, but I recommend giving safflower a try. The dried flowers, not oil.

Using dried safflower in combination with a small quantity of both turmeric and msg, you can somewhat reproduce the effect of saffron as far as color and flavor enhancement. This can work in chicken soup / chicken pot pie. Do it when you're in a pinch for money, don't have saffron on hand, or if you want to try a slight variation on a recipe you already like.

I'm mildly surprised no one else has mentioned safflower. So, I'm posting this answer more to contribute information than to try and win in the best answer contest. Because, truly, there is no good substitute for saffron - especially when you're talking my favorite dutch pot pie recipe. Which (there being no good substitute), is I assume why so many vendors get away with charging so much for saffron. That, along with an involved production process.

Supposedly, (wikipedia, etc) some refer to safflower as "bastard saffron". But, safflower is far less strong, has a sage-y presence (imo) rather than savory like saffron. Hence my suggestion to use it with Accent/msg if you're trying to reproduce that savory flavor with meats. The main thing that's nice about safflower is the similarity in color and (somewhat) appearance of yellow-orange-red fibers which is similar to saffron, perhaps especially when cooked in a wet dish like soup or saucy meat.

Aside from the issue of mimicking saffron, in my experience, using dried safflower is best when cooking Mexican dishes - such as shredded chicken for enchiladas and burritos. This would be more for a yellow/red effect with paprika and green chile, and not for a full green salsa verde recipe. Safflower has become a staple ingredient in my cupboard. In the Western USA, it's available in many grocery stores in small 0.25 oz packets. For other regions, it looks like you can order it on Amazon (in bulk).

I made a lovely Paella tonight with Laotian sausage, paprika-and-salt dry-rubbed chicken drumsticks, and a 1/2 pound of shrimp (shrimp added to rice mid-simmer). Finely diced garlic, red onion, heirloom cherry tomatoes and a red bell pepper and jumbo carrot was used to make a sofrito in the meat drippings after deglazing with Marsala. I had some tomato and cream soup in the cooler, and used that and some water as liquid for 12oz. of long grain rice (start with 3 cups liquid total, add a little more to further soften the rice if needed). As I did not have any saffron on hand, I used SICHUAN OIL instead (one table spoon). The flavor profile of Sichuan is a hint of lemon zest, and a mouth feel of mild numbness combined with the perception of phantom saltiness which leads to a rounder, meatier flavor, much like Umami.

A few other flavors that are part of my typical bouquet came from some dashes of fish sauce, and leftover soy sauce and capsicum chili oil I had used to marinate raw tuna slices as a snack while cooking. Waste not, want not, and it made things even MORE delicious!

Try the Sichuan oil, available at many Asian stores and online. Dry berries are less effective, and fresh are not available Stateside. You will find yourself adding it to MANY things!