Alex, as I learned the story of Caesar Cardini's extempore origination of the Caesar salad, it DID have the anchovies. One of us is wrong!
I can't stand anchovies straight--MUCH too salty. But in Caesar salad, yes. The trick is to mash them up and incorporate in the dressing. A little of the flavor, but not enough to kill you.
The one other place for anchovies, in my book, is a pasta dish my Beautiful Wife makes, with cauliflower flowerets in a sauce with a little anchovie flavor. For this I give her my supreme accolade: "You can make this ANY time!" When she hears that, she knows she's made a hit.