Sometimes and sometimes. If I know something important happened in so-and-so's area yesterday, I'll look at the aggregated tweets for yesterday, or if someone says "oh, just check Twitter", I'll scan through that person's posts for an explanation. Since I very rarely use Twitter anyway - I'll have a few weeks of checking it every other day or so, then I'll forget about it for a few more weeks - it's nice to be able to skim a collection of tweets and see if anything interesting was said.