From a chemistry point of view, pouring developer down the drain is not nice, but not too terrible either, at least with hydroquinone-based developers. Hydroquinone occurs in nature, which is why you can develop in coffee. It also occurs in the digestive tract. To put it frankly, the day after an evening with a good number of beers you're likely to deposit more hydroquinone into the sewage processing system than if you pour in a shot of used Rodinal (in theory you could develop in feces, which in practice, however, nobody seems too eager to do). In quantities from a hobbyist lab, the active substances from used developer are likely to be broken down already by the time they reach the sewage plant. However, given that you should turn in your used fixer anyway, you could collect your used developer, too.
Stop bath is usually a very weak acid, such as citric acid. This can be safely poured down the drain. If you're worried, you can use water as a stop bath. It will do the job, too. There are residues of developer in the stop bath, but we are talking about negligible drops.
The worst thing to pour down the drain is fixer, as it contains silver which is detrimental to the bacteria doing all the work in your local sewage processing plant. In theory, you can get the silver out of the fixer at home using sodium dithionite (leave it in the open, as it will produce sulphur dioxide) or using iron wool. This is what Kodak calls silver recovery. In practice, Kodak's recommendation is geared at medium-scale to large-scale labs. For a home lab, getting the silver out of the residue by smelting is complicated enough and produces so little quantities that it may not be feasible. The alternative is to give the fixer to whatever municipal authority is handling it in your case.
The thing Roger wrote about silver being heavy ignores that the silver is bound and in solution. If it would sink down on account of being heavy, all the heavy sodium cloride (specific weight 2.17 g/cm³) aka "salt" in the oceans should sink down to the bottom. Somehow it doesn't. Silver is indeed hazardous to microorganisms, which is why it is used to clean biological contaminations from drinking water. In the case of a sewage plant, however, you're interested in the survival of these microorganisms.
