The proper way to read Twitter is to “dip into the stream” to read and view whatever is currently flowing by. It's considered to be adding unnecessary stress to your life to try to read back and catch up on your stream.
I agree. However, if you are using Twitter as I am, i.e., as your main source of pointers to news and anything interesting, you may want to scroll back and read previous tweets from some of the accounts that you're most interested in. A good example might be @Slashdot.
The reason is simple. Due to the real-time nature of Twitter, if you read posts at a particular time of day, you may miss most of the items by a user who tweets at a different hour. @GuyKawasaki tries to fix this for you by repeating his tweets several times throughout the day. I supposed that's okay, though it makes him sort of noisy.
Currently I just wait until I come across a tweet by one of those accounts I find interesting. Then I just click on the id and read back through the tweets until I become bored, tired of them, or see repeats. Of course you can just scan down the list to see what's interesting.
That's working for me now. Another approach would be to create Twitter lists with these accounts, or even one big list. In fact, that's probably the recommended solution. My approach has the advantage of being dynamic and doesn't tie me to a fixed list, so the sites I consider interesting can vary as rapidly or be as constant as I wish.