#1 Rapidly Climb Learning Curves
The ability to quickly learn enough about new subjects to be useful. New technologies or APIs; new algorithms; mathematical or statistical subjects; and most importantly, your problem domain. Some of this ability is a skill, "knowing how to learn", which covers google-fu, reading comprehension, prioritization, time management, etc. Some of this ability comes from having enough aggregate experience that new information just clicks into place like jigsaw puzzle pieces. Some of this ability comes from the confidence of having climbed enough seemingly insurmountable learning curves that this next one is "just another day at the office".
A sign you're doing this wrong: "I need training!"
#2 Understand The Customer
IMHO, the best engineers are half product managers. You can easily get a 10X improvement in productivity by building the right features and not building the wrong ones. Yes, professional product managers are great, but technical limitations often impact product design. A great engineer knows when to push back or suggest alternatives. This requires empathy not only for the customer, but for the product management team. This ability is also tightly coupled with #1 - you need to quickly come up to speed on the problem domain, whatever that may be. If you wan't to be a great engineer, don't study algorithms (until you need an algorithm, of course), study the particular business that you're in.
A sign you're doing this wrong: "Whatever, just tell me how you want it and I'll make it that way!"