Here's a pretty good list of what not to feed and why:
Never give: Why not?
blue cheese contains toxic mold
licorice contains a suspected neurotoxin
raw dry beans or peanuts contain antinutrients, cause red blood cell
clumping (note: the peanuts that you buy in stores are almost always roasted so are okay.... frozen beans from veggie mixes are okay because they've been pre-cooked)
raw sweet potato contains cyanide-forming compounds
raw red cabbage and brussel sprouts contain an antinutrient that destroys thiamin
raw artichokes inhibit protein digestion
green bananas inhibit starch digestion
green potato skin and eyes contain solanine (toxin)
wild insects could carry parasites
rhubarb high levels of oxalates which bind up calcium
raw bulk tofu can contain bacteria (packaged tofu is safe)
orange juice contains d-limonene which can cause kidney cancer in male rats
raw onion can lead to anemia and an upset stomach
If you want to let your rat try these, be careful: Why?
carbonated drinks rats can't burp!
chocolate It contains stimulants that can lead to heart failure or neurological poisoning in high quantities. A bit of chocolate is okay and can actually temporarily alleviate respiratory distress
Peanut Butter This can cause choking in rats. If you want to give your rats some, mix it with jam or something liquid to make it less sticky.
Avocados These are high in fat and are a good treat to feed rats that are in need of "beefing up" (make sure the fruit is ripe). However, the pit, rind, skin and leaves of avocados are toxic. The part of the fruit in contact with the pit has a higher concentration of toxins.
dried corn It can have high levels of fungal contaminates which can lead to liver cancer. A little fresh corn is fine.
Other things to watch out for: Why?
Mold This can be toxic. You wouldn't eat a moldy piece of food so of course you'd never give it to your rat. Remember grains can go moldy too.
Chlorinated and/or fluoridated Tap Water Chlorine isn't good for us or our rats. Read more about the dangers of fluoride here.
Household Plants Here's a list of toxic plants: Plants that are poisonous to small pets. Be sure your poinsettia and holly are out of reach over the holidays. Note: in some cases, some parts of a particular plant are poisonous (eg. foliage) whereas other parts of the fruit are safe (eg. fruit).