SL, you're right about the ang moh's being better at tooting
their own horn.
If you work in an American firm
with a high proportion of expatriates, you graudally learn to do
that too, without wincing. hehehe! 
I've been on both sides of the table - I've been the candidate, as
well as part of the interviewing team. Some observations :
- NEVER appear scared! I've seen candidates shivering, literally
shivering.
Half your battle is lost already because
what happens next would usually be stammering, stuttering,
requesting simple questions to be repeated followed by a long lag
time before an answer is given, etc. A "What's happening, cat got
your tongue?" kinda situation.

- Tell yourself that you're a professional and you're NOT DESPERATE
for the job. It's ugly when you see how desperate some candidates
can be.
Sit back comfortably in your chair, be at
ease, and remember that like neuros said, you're interviewing the
interviewers as well because hey, you're a professional, you have a
right to choose the best job and the best working environmnent for
you too!
That will immediately up the ante on your
side and change the entire 'tone' of the interview because then,
the interviewers would know that here's someone who's interested in
a career and professional development and not just a job.
- Memorised 'stock' answers are blah! The interviewers would have
heard the same 'stock' answers a thousand times before you and if
you give them the same ol' humdrum stuff, they'll immediately shut
you off mentally and you'll be no different from the hundred before
you.
So, dare to be yourself. Offer
answers that are unique because they're not the 'typical'
answers.
Lastly, remember that there are lots of reasons why a candidate is
not chosen for the job. Sometimes, you'll be surprised, it has
nothing to do with you even! I know for a fact that there are firms
in Singapore that go through the recruitment process even though
they already have an internal candidate in mind who's snagged the
job 99% already simply because it's a process / policy they have to
adhere to.
Sometimes, they choose someone less vibrant
because they might think that the person would have a higher chance
of staying on in the job, which might turn out to be pretty
monotonous in reality. Etc. etc. I can give you a few other
scenarios so yeah, don't take rejections personally because it
might not even be about you! 
One of the most challenging interviews I went for started with
grouchy interviewers firing this question at me, straight-faced,
'So, tell us why we should hire you.' I was
but kept my cool composure and I guess they
liked my answer cause in the end, I got the job! 
Have courage! 