The solution for this is something called RSS, which is a way for content providers to provide an index to their content.
I run a program which scans the RSS feeds for all the blogs I have subscribed to, and I get a list of the posts which are new since the last time I looked. Right now, 5 out of the 21 blogs I follow have RSS feeds.
Calling all bloggers, please please please check with your blog software to figure out how to generate an RSS feed. I am currently using TypePad for my faith-rambling blog, which is a subscription service and it provides an RSS feed for everyone. I understand that currently blogger/blogspot only provide RSS feeds for the "Pro" level blogs. I don't know about any other blog services.
For Mac users, the software I am using to both read AND post to all my blogs is NetNewsWire. Sorry, don't know what PC users are doing.