The classic Caesar is quite different than modern-day interpretations that most people enjoy. At some point in time the dominant flavors found in the traditional worcestershire sauce (anchovy and garlic) saw direct use and whats-that-here sauce saw a decline in use. Also, the dressing that forms on the romaine by tossing egg yolk, lemon juice, and olive oil was divorced from the greens and constructed on the side. Personally, I like the dressing made on the side - as you have better control over it's outcome given variances in lemon acidity, yolk size, and moisture. Essentially it's a thinned mayo flavored with garlic (paste), anchovy (paste), lemon, black pepper, and parmesan (which I add both to the dressing and atop the salad in different forms). I also use a touch of dijon. I've tasted Caesars made with all sorts of oil, and I think Olive Oil tastes terrible in a Caesar. Personally, I prefer a neutral flavored oil such as Canola.
I love it with charcoal-grilled butterflied chicken breasts that are marinated in a bit of lemon juice, dijon, garlic, black pepper, and neutral-flavored oil.
While I used to make lots of garlicky croutons to toss with it, my fiancee doesn't like the crunch as much and asked me to make a garlic bread instead. I was hesitant, but after trying it with charcoal-grilled slices of fresh bread brushed with garlic butter I'll never go back!
Personally I've actually grown apart from the "Caesar" flavors and piles of Romaine. Caesar dressing also pairs very
well with fresh tomatoes and bacon. Whenever I'm craving Caesar flavors I now make a Caesar BLT. It features the above garlic toast brushed with a Caesar mayo and filled with lettuces, thinly sliced tomato, and crispy bacon. I even use a tablespoon or so of the rendered bacon fat to make the mayo...
It's my favorite sandwich next to a great burger.