First off let me say I am NOT a neat nick germ-paranoid sort - I am known to eat things off the ground and am most certainly a dirty-girl inside caves etc. Living in the tropics however brings about some new cleaning issues that have taken time to resolve. I have consolidated some of my solutions to the problems you get living with constant warm, humid weather.
Bleach seems like an obvious thing. I am not a fan of using chemicals and I generally dislike anything scented including sprays, candles, deodorants, laundry soap and on and on. Bleach I have found is a true necessity. What do I use it for? For starters I use it weekly for the dish drainer and sink. I do not have (nor want) a dishwasher but that white dish drain thing sitting there on the counter gets all kinds of black stuff on it. It is only clean dishes going there but still, the black stuff. I soak it in a rinse bin of bleach water and use these handy little brushes (or a toothbrush) to brush away the crap. Then I plug the sink and empty it into there to disinfect and de-stink the sink! Another important use is to put a few drops into bird baths, cat water dishes and other places you have water standing (big pothole outside in the road). This kills mosquito larvae. It is good to have bleach on hand in case you need clean drinking water if there is a hurricane. If you can't boil, then do one part bleach to 9 parts water and let it sit for a bit. FEMA recommends filling the empty bleach container with water and that is enough to disinfect it for drinking.
These slim brushes get inside the S blade contraption of your food processor or around the faucets or the ice dispenser of the fridge.
Dish soap is great for rotten ants. They don't seem to like to cross a line of it and I take great joy in drizzling it over nests that have popped up where I don't want them. Yes, I have a problem with ants.
The Magic Eraser is a super cool thing made from a natural stuff (forget what, I looked it up once) and it is great if you get moldy spots on your ceilings from high humidity. It is also great to clean up sinks and sports gear. I like this thing. It helps clean out the little drip tray on the fridge where the ice comes out.
Goo gone should be used sparingly since it is probably petrol solvents or something awful. It does have a couple good uses here in Puerto Rico. One is to get the Marbete sticker residue off the windshield (or any other sticker off anything) and another is to get latex off machetes and knives. A lot of the fruit here is latex heavy (canistels, panapen, green bananas, platanos) and this will clean up your tools.
The bleach pen dispenses bleach in a gel form so it will stay put on grout, ice dispenser trays etc.
Green Works seems like an ok coconut based cleaner but it is really the spray bottle I am after. I put one part bleach and 9 parts water in it and spray it on shower curtain liners, grout and anything moldy. I have a second one with vinegar (I'll get into that later).
Vaseline seems like a crazy thing but it is great to put on your refrigerator seals so they don't crack. Anything plastic or rubber is a problem here but with a little vaseline... less of one.
Finally my favorite discoveries...vinegar. Vinegar is a great cleaner and a wonderful de -stinker! If you have a lot of sports gear that goes into caves or salt water, or have a lot of cats and nasty cat boxes give your stuff a soak in laundry detergent with some vinegar added. The vinegar takes out the pee smell, ammonia smell, and sitting around smells that neoprene tends to collect. It is also a great all purpose window, mirror, bathroom cleaner that I put in a spray bottle (diluted of course). Best of all, SAMS club has it in big jugs...
So that's it for my tips. My pet peeves were the ice maker lever and drip tray and dish drainers. Also getting cat smell and neoprene smells to go away...any tips you've got I'd love to hear about!