My top 3 are probably calve's liver, chicken livers, and properly prepared tripe. If tongue and bone marrow count, I'd add those. I like heart too (venison, beef, or pig), but it is really just a tough muscle so isn't really offal.
A trick for liver is to soak it in lemon juice for about 30 minutes before cooking it, this cuts out many of the "off" flavors and also helps to expel any residual toxins that might be present. Fried in bacon grease or lard and left medium-pink in the middle it is delicious.
I agree with what the previous poster said about liver being nature's multi-vitamin. I get liver cravings at least a few times a year, and it is the only dish that, about halfway through a portion, I feel that "kapow" of satiety, I just feel that my body is rapidly absorbing the nutrients.
Chicken livers are so absurdly easy to prepare, and cheap, that they should be in the heavy rotation. You can make a pate in literally a few minutes by sauteeing them with onions, garlic, a bay leaf, maybe some other spices, and giving it a whirl in the food pro. This goes particularly well with raspberry jelly (unsweetened of course).
Tripe when it is well prepared is one of my all time favorite foods, if done right it tastes like perfectly al dente noodles (but without the yucky starches). When not so well done, it tastes like rubber. Preparing and cooking it is both labor intensive and stinky, so I try to find it when I go out. Of course ethnic restaurants are the only way to go because lame Americans don't eat it.
I like kidneys well enough but even with perfect preparation they smell and taste faintly of urine.
I was in Chinatown recently and ordered something billed as "crispy pig intestine". I was hoping for something along the lines of cracklins, but it turns out it was the (too-) briefly fried LOWER intestine of the pig. Yep, it smelled and tasted faintly of pig poop, and was chewy and rubbery to boot. Don't think I'll be ordering that one again.
If you're a fan of the offal you have to check out this blog, she has some great preparations of brain, kidney, sweetbreads and pig face (yep, pig face):