5 Foods to Never Refrigerate...

Although there are plenty more that can be added to this list...a look at the site kitchendaily.com, shared this information, but here they are;
Avocado: best if used just when beginning to soften,. sometimes the seed inside will even rattle a bit if it is at ripeness perfection. Remember though, that once cut the avocado flesh will darken when exposed, doesn't mean its bad, but really isn't the most attractive to eat. I let them ripen along with my bananas and other fruit, on the kitchen counter.
Basil: placed in a glass of water, (or a small vase, just like fresh flowers), allows this herb to breath and not get damaged by the moisture and condensation in the refrigerator, and just like cut flowers, change the water often.
Tomatoes: Fresh off the vine or store bought, tomatoes do not like refrigerators. The texture and taste quality is diminished greatly.
Onions: Again, the moisture from the refrigerator allow them to go bad faster, so best in a cool dry place...except when cut, then the refrigerator is your best bet for the leftover.
Potatoes: Refrigerators wreck havoc on them. Definitely deteriorates the texture and taste. Another one that is best kept cool and dry.

I also keep out my garlic, there are those who refrigerate, but it seems to make it harder to peel and I think it affects the texture and allows for mold. Realistically, garlic never lasts that long at my house, so its best to have it handy. A garlic pot or stored with my onions is how I do it.