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On the internet in general? Very little, I would think.
On people who think Yahoo is important, like for thier email or their chat groups/forums etc, it could have a significant effect. Microsoft, as far as I know, duplicates everything Yahoo does, except maybe having a well known search engine. I would expect all those Yahoo services to eventually disappear, in favor of pushing people over to the similar Microsoft services. In the long run, Yahoo will no longer exist.
I was having a conversation with a co-worker just last week about yahoo. We came to the conclusion that Google or MS would eventually have their way with yahoo.