Usually there are six to avoid.
E102: tartrazine
E104: quinoline yellow
E110: sunset yellow
E122: carmoisine
E124: ponceau 4R (banned in the US for many years & considered dangerous)
E129: allura red
The main issue with these is ADHD. So usually there should be a mandatory Warning on the label. I am not saying that there are other factors which are shown below, but there are arguments and disagreements.
However, many think these two should be considered dangerous and avoided -
E102 Tartrazine is a water soluble Azo dye (Trisodium (E)-5-oxo-1-(4-sulfonatophenyl)-4-(4-sulfonatophenyl) diazenyl)-4,5-dihydro-1H-pyrazole-3-carboxylate.)
is said to increase Thyroid tumours, and might cause anxiety, migraines, clinical depression, blurry vision, ADHD in children etc.
E122 Carmosine - Another Azo dye, Red in colour containing two Napthaline subunits. Suspicion of bladder cancers, Asthma and ADHD in children.
Generally azo dyes are suspect carcinogens.