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From time to time I see strange Twitter handles following me on Twitter. I generally ignore them. Don't follow them (for sure, don't even look them up mostly).
What can be the intention of these other than they are expecting me to follow them or the links they post?
Is it safe to ignore them (and let them continue following me)?
In reverse order:
Yes it is safe to ignore them. People can't see anything more about you if they follow you than normally. You can only be DM'd if you follow them back.
Their intention is to spam your Twitter stream with adverts - which they can only do if you follow them back. I think that there might be value in accounts with many followers so they may also be doing this in an effort to create an account they can see on to someone else.
So just carry on as you are. In fact if you don't follow back there's a good chance that they'll unfollow you fairly quickly.
As Eight Days points out - you should consider reporting them to Twitter as spammers.
If you are really paranoid protect your Tweets.
