This is a very common question, and has always been a very real concern.
I've only been using Linux since mid 2009 (started out with the horrible 09.04
and 09.10 versions), and did a lot of research as to the different flavors of
Linux (I've standardized on Ubuntu, but do play with others for my own
edification). I also researched the differences between the 32- and 64-bit
versions. (I was surprised to find out that until recently, a 64-bit version of
Windoze was either non-existent or quite rare.)
From what I've been reading over these past couple years, software writers are
playing catch-up with regard to coming up with 64-bit versions of their drivers
and programs. Flash has been a real concern because Adobe did not yet have a
mature 64-bit version for Windoze, and certainly didn't have a Linux version
that worked (concerns with Adobe were also for functionality and all their many
security flaws).
I also read that a 64-bit OS will also run calculation-intensive applications
much much faster than 32-bit (it's not a linear relationship: 64-bit is not just
twice as fast as 32-bit, but can be much much faster, such as 10 times or more).
Us mere mortals do not run calculation-intensive applications such that we would
notice, but still, I wanted the "future standard" so I could learn it.
So I did it.
Contrary to all the "go with the 32-bit" advice in the many Linux forums, I
forged ahead and went right to the 64-bit version because that's what my laptop
and desktop were, and that's where the technology is headed anyway. Along with
many other people and companies, I hated Flash anyway, so if it didn't work I
didn't really care because Linux was that important to me.
Some web sites that are Flash-intensive, and are written with Windoze in mind,
indeed do not work or don't work perfectly in my Linux; I don't care. I always
keep my OS (presently at 11.04 and holding indefinitely) fully automatically
updated, and that always includes the most recent Flash.
My printer and wireless always worked perfectly with Ubuntu. (I couldn't get
openSUSE to work with my wireless.)
So I consider my 64-bit Ubuntu experiment a success.
I would suggest you go for it; install the 64-bit version to push the technology
and demonstrate the demand for 64-bit support. If you have any problems just
install the 32-bit version and see if it works any differently. It's free; your
only expense is the investment of your time.
---
As an aside, I do participate on-and-off in distributed parallel processing
projects (no silly ones, just meaningful ones) from BOINC...
http://boinc.berkeley.edu/ , and it does involve integer and floating-point
calculation-intensive applications that will pin both cores of my Athlon64 at
100% for weeks at a time.
Making measurements from their site, and comparing my modest 5-year old desktop
computer to other volunteers running 32-bit and 64-bit Windoze, my 64-bit Linux
is blistering fast!!!
Credits are given as a function of the number of calculations that are performed
and projects completed. My modest computer running 64-bit Linux quickly rose
through the ranks, and was in the 99th percentile of all users world-wide
regarding "recent average credit"; I was at the 96th percentile (and rising) of
all users world-wide in regard to the total number of calculations performed.
Even on an aging, modest computer, Linux Rules!!!
I also replaced my CPU cooler with a significantly better one that has more fins
and a lot of copper (for only $15 from the local computer store!!!), and my CPU
core temperatures dropped 20 to 30 degrees Fahrenheit when both cores are pinned
at 100% for extended periods of time; money well spent!