We were actually surprised to hear this question when we lectured last week at the Indiana Bar's Solo and Small Firm Conference. It's not surprising that large firms feel the need to archive postings, but it was striking that a solo attorney should feel the need.
Not only did a member of the audience bring up the possible ethical need to archive postings (I am unaware of any state that requires this but am willing to be educated if I'm wrong), but they wanted to know how they could securely delete social media postings. That is a lot harder - each social media provider has a different way of storing postings - the fact that you can no longer see a posting doesn't mean that the provider hasn't stored it. More fundamentally, once posted, you have no idea who may have copied it, forwarded it or stored it for their own reasons. This is why it is best to take the view that whatever you post will live forever - somewhere.
In terms of technologies to archive social media postings, Rob Robinson of Orange Legal Technologies has compiled an excellent list for you to check out.
There are many business intelligence reasons to archive the social media postings of others. You can gather information useful in litigation or just learn from your competition. Does Pepsi monitor Coke? I've no idea, but it sure wouldn't surprise me.