I don't usually laugh at people falling down or getting hurt. But that picture bwinton just posted made me "bust a gut." After catching my breath I began to wonder why that picture is funny to me when usually pictures like that just make me feel bad for the soon to be wounded. Then I realized it is the umbrella. No umbrella=just another picture of a guy taking a header. With umbrella=comedy! Maybe that alone is a good reason not to carry an umbrella?
Seriously though, I think an umbrella on a bike is a bad idea. You're still going to get wet. Plus I don't like to think about what would happen if the umbrella were to get caught in the spokes.
When I wore glasses I found that water got on my glasses to some extent no matter what I did. Buy one of those microfiber glasses cloths and keep it in a pocket of your rain jacket.
If you ride a lot, especially for transportation, a good rain jacket or rain suit is well worth the investment.
bwinton,
That is a great avatar!