Blogging is not for everyone and you don't want to give the impression you are something you are not doing something right if you don't blog. Not everyone is a writer, not everyone likes putting their thoughts down, and not everyone is brave enough to publish out on the Internet.
It takes a thick skin, and even after doing this for years, I still get attacked regularly, and I don't always take it well. I'll admit it gets to me. Luckily I have a good support system with my wife and friends that can pick me up when I've had a particularly nasty comment.
I do a presentation on The Modern Resume, telling people how to big a more noticeable presence in the world, making yourself stand out more. I think blogging is the easy way to do this, but there are others:
I don't think you can get away from writing completely since you'll need to document and explain things you've done. However it can be as simple as notes you've made to yourself and a few lines on your resume or CV.
Writing is a skill, however, and I'd encourage you to develop it. If you don't want to blog, it still makes sense to pay attention to how you communicate in email, in reports, and in documentation. Learn to do it better and your career will benefit.