Yes, produce gets gas too! Several fruit and veges produce ethylene gas – a hormone that accelerates the ripening process. That means if they're stored with ethylene-sensitive produce, they'll cause them to ripen faster or cause them damage (ethylene can change flavour, texture, colour and cause some leafy greens to droop). So you'll need to be strategic with your storing to prevent rapid ripening. The best way? Put simply - separation. Keep your ethylene-producing produce away from your sensitive types.
Take apples - a prime ethylene producer - for example. If you're storing them on your bench, keep them in a separate bowl or in a paper bag away from other fruits. If you're storing apples in the fridge, put the apples in a separate tub, bag or drawer.
Conversely, if you want your fruit to ripen faster, you need not worry too much about letting your gassy fruits mingle with your other fruits. But you'll need to keep an eye on any damage forming. 
Just some of the produce that produces ethylene includes apples, bananas, avocados, blueberries, grapes, mangoes, mushrooms, pears and tomatoes. And ethylene-sensitive produce includes broccoli, carrots, cauliflower, lettuce, potatoes, cucumbers and cabbage. Click the link for a full list of ethylene-producing and ethylene-sensitive produce.