Baking Soda and Lemon should be on the top of your list.
There are different solutions to use based the situation.
I have found the following site useful for a more natural and safe way to clean food and stuff around the house, http://eartheasy.com/live_nontoxic_solutions.htm
sustainability.stackexchange.com/users/22/Colby Guyer
In addition to Baking Soda and Lemon, as @Colby mentioned, I'd add that Vinegar will clean most everything; it is non-toxic and cheap.
I've found it to be very effective for getting rid of molds and musty smells.
If you get Vinegar on your food, who cares, right?
You could still eat it, unless you don't like the taste.
sustainability.stackexchange.com/users/69/BryanH
I'm in the cleanliness is over-hyped in our culture camp, so I probably have a different outlook than you.
But, I wash surfaces mostly with just water and a cloth.
If there's grease to cut or I want to damage microorganisms, I'll wipe down with vinegar.
I don't even use baking soda for surfaces -- just for burned pans and such.
This mild sanitation protocol works well even in my kitchen which is deeply saturated with microorganisms due to years of various, constant fermentations.
sustainability.stackexchange.com/users/115/clweeks
You'd be surprised how much you can achieve with a piece of cotton, clean water and much patience.
While camping, we're cleaning all pots with water and a piece of grass or leaves.
It requires more time than using detergents and hot water, but it is possible.
Fats don't dissolve in water, so you can use a bit of alcohol for them.
Home-made , of course :)
sustainability.stackexchange.com/users/5/Danubian Sailor
If you want commercial products check out Good Guide , they rank products based on ingredient hazards and larger environmental impact.
They have an extremely large database and rank things from cleaners to food to makeup.
sustainability.stackexchange.com/users/4973/akb
I'm wondering what kind of products I can use that are not dangerous to keep kitchen surfaces clean and safe.     Should I get different products for different types surfaces (e.g. granite top vs. wooden cutting board)?    Should I get different products for different types of foods (e.g. meats vs. vegetables)?
What non-toxic products can I use to keep my kitchen counters clean and safe?
sustainability.stackexchange.com
<cleaning><hygiene><safe-chemicals>
sustainability.stackexchange.com/questions/8
sustainability.stackexchange.com/users/20/WilliamKF
Various solutions may be used depending on the situation. Baking soda and lemon are at the top of the list, although vinegar or clean water and a cotton cloth are also recommended. It depends on the situation, but you could use items such as baking soda, lemon, vinegar, cotton and clean water.
Possible solutions will depend on the situation. Baking soda, lemon and vinegar are useful. Cotton and clean water can be helpful.