I started typing, and realized I have too many opinions about this. I'm sorry.

Vinegar is decent at dissolving sugar, and in that context it works really well for what it is. I usually buy a big jug of it for both cooking and cleaning, but a general purpose cleaner it is not. Side note, adding a small amount to ground meat helps the meat flow a bit better for meat pies or taco mix.

For grease and grime cream of tartar works really well. I cook with stainless steel and sometimes egg or something will burn and stick to a pan. I throw a whack of cream of tartar in the pan along with some water and the pan will pretty much self clean on the stove.

If you're doing dishes by hand because dishwashers aren't meeting your expectations, there's a Technology Connections video about using dishwashers that's worth a watch if you've got 45 minutes to spare and don't mind watching a midwesterner beat a topic to death in the best way possible. Eco-friendly powders exist. Really, the appeal of a dishwasher is to use the mechanical force of water to clean.

For purely antibacterial you just ain't gonna beat alcohol. I mean... it's used at hospitals. For glass cleaning a 50/50 mix of distilled water and pure alcohol won't leave streaks.

A mix of lemon juice and baking soda will get rust stains out of some surfaces. Baking soda paste, followed by some vinegar will clear out toothpaste in a drain.

Probably the harshest chemical I use is bleach, but I only use that for the toilet. Easiest way to clean porcelain by far, and you don't need that much... and really it's kind of a set and forget thing.