Homemade or store bought? Read on:
You're more likely to get food poisoning from contaminated meat or veggies in those salads than the mayo.
First, what is in mayonnaise? Oil. Vinegar. Lemon juice. Raw eggs. Salt. Spices. As we can see, most of this stuff won't really spoil. Everything but the raw eggs. Ah! But, in commercial mayo, the eggs are first pasteurized so they are CLEAN. Then we have the vinegar and lemon juice. Mayo is actually pretty acidic.
From Hellman's website, they state it should be refrigerated as higher temperatures will affect flavor. No mention of spoilage. But, to really get the facts, we go to the Association for Dressings and Sauces. Yes, it exists. They state mayo gets a bad rap. Most likely because homemade mayo is made with regular raw eggs which makes them very perishable. But, as stated, commercial mayo uses pasteurized eggs. The issue is cross contamination of other ingredients. Mayo isn't strong enough to kill new bacteria introduced into the salad. So, that pasta salad without mayo will go bad if you have other bad ingredients.
http://whatneedsrefrigerating.blogspot.com/
That common misconception dates back to the days of homemade mayo. Today's commercial pasteurized mayos are very safe. That being said, potato salad shouldn't be left at room temperature for too long, because the potatoes are still a breeding ground for bacteria.
http://homecooking.about.com/od/howtocookwithcondiments/a/mayospoilage.htm