<p>When coding, what is a good rule of thumb to keep in mind with respect to performance? There are endless ways to optimize for a specific platform and compiler, but I'm looking for answers that apply equally well (or almost) across compilers and platforms.</p>

The number #1 performance tip is to profile your code early and often.  There are a lot of general "don't do this" tips but it's really hard to guarantee this will impact the performance of your application.  Why?  Every application is different.  It's easy to say that passing a vector by value is bad if you have a lot of elements but does your program even use a vector (you probably should but ...)?
Profiling is the only way to understand the performance of your application.  I've been in way too many situations where people "optimized" the code but didn't ever profile.  The "optimizations" turned out to introduce many bugs and not even be a hot spot in the code path.  Waste of everyones time.
EDIT:
A couple of people have commented on the "early" part of my answer.  I don't think you should be profiling from day 1.  However you should also not be waiting till 1 month from ship either.
I usually first profile once I have a couple of definitive end to end scenarios, or in a larger project, a mostly functional component.  I take a day or two (usually working with QA) to get together some large scenarios and throw it at the code.  This is a great spot check to find obvious performance problems early.  Fixing them at this point is a bit easier.
On a typical project I find that I have code meeting this criterias 30%-40% of the way through the project (100% being in customers hands).  I loosely classify this time as early.