I am using CiviCRM 4.7.7 on Drupal 7. I want to send an e-mail to each contact added "Today". So I supposed to create a smart group with the search criteria "Added=Today" in the "Change Log" section. I suppose to create this smart group today, i.e the June 6th, 2016. Tomorrow the smart group criteria will be always the June 6th, 2016, and not the June 7th, 2016, as I would like. Can someone help me?
So, I might not be able to answer the question regarding the smart group criteria required to set the date always to 'today' (I had a look into this and confirmed your description that the criteria gets "translated" from 'today' into the date for today, and will remain that way afterwards).
However, if you're looking to send an email to each contact created in the system then you could look into using the scheduled reminders system for this. Under Entity you can select Contact > Created date only, which might help with your scenario.
The downside to this though is that you'll need to be sending out the same message to each user (although you can use tokens to personalise this!).