SimCity 4/Sanitation

All buildings in the game produce garbage, and if you do not have a way of disposing of the garbage, it will pile up in your city, which results in a low desirability and a negative Mayor Rating.

There's a very easy trick to get rid of garbage: build a Waste to Energy plant, then click on it and use the slider to set its funding to §0. Even though it won't generate any power this way, it will still incinerate your garbage for free. You can also use it as a reserve power unit like this should you run out of power and be unable to afford a new power plant at some point.

If you decide to not use this trick, the game has only a handful of means available to get rid of garbage. Note that SimCity 4/Ordinances can help reduce the amount of garbage in your city.

Landfill
The landfill is, simple enough, a zone much like residental or commercial zones, only that its purpose is to store garbage. While a landfill may be acceptable for a beginning city, as it grows larger your landfill will pile up and the maintenance cost will rise to levels where it is simply no longer economical. Since the landfill has a strong negative effect on desirability, you should zone it away from residental areas and near your industrial zone. Note that the landfill is a bit weird when it comes to road access; it needs a road along at least one entire side, otherwise the connection will not be recognized.

Garbage stored in the landfill decomposes over time, at a rate of 7% every month, but with an upper limit of 15 tons. This means that letting a landfill decompose completely on its own takes a very long amount of time. If you intend to do this, it is recommended to cut off road access to prevent any further garbage from being stored in the landfill, which will just extend the duration needed. Empty landfill tiles can then be dezoned with the dezone tool.

Recycling Center
The Recycling Center will reduce the amount of garbage by 20% for every 25,000 people in your city. However, its very high monthly cost usually means you'll only be able to afford one when your city is already quite large.

Waste to Energy Plant
The Waste to Energy Plant burns up to 50,000 tons of garbage per month to generate power for your city. While it generates lots of pollution and its efficiency isn't that great, it's the only long-term viable solution to garbage disposal in the game.