That question, to me, is like asking "What's your favorite movie?" With the SI, we are actually able to taste the nuances of different smoke flavor in the meat, as it's not part of the heat source. On traditional smokers, I have never really been able to tell the difference between some....but now I can!
So, my favorite woods may be significantly different from yours, or vice-versa! I treat wood smoke flavor just like any other spice, for the flavor it imparts to the meat. The
only way to find what you like is to
experiment! For example, lots of folks say hickory and mesquite are "too strong," but I don't think they are! In fact, if there was only wood I could ever smoke with again, I'd choose hickory, hands-down! That's because I grew up in the south where hickory was the standard, so it "smells like BBQ," to me! Others have different experiences with different woods. Another example is apple; love the smell of it, when it's smoking, but really dislike the flavor profile it gives meat! See what I mean? You can't turn on the TV with seeing some commercial about "Apple-smoked (fill in the blank)." Fact is, I don't like it, but many do.
Now that I've given my 2¢ on wood philosophy, I'll join in the fun!
Beef: Hickory, mesquite, red or white oak (depending on the recipe. Red oak is a little stronger flavor than white oak).
Poultry: Hickory, cherry, ash, maple
Pork: Cherry and hickory, pretty much exclusively! I've used white oak, and it's also good, but I stick to cherry and/or hickory.
Cheese: Hickory or cherry.