Calculated Column Values Only Recalculate As Needed
The values in SharePoint columns--even in calculated columns--are stored in SharePoint's underlying SQL Server database.
The calculations in calculated columns are not performed upon page load; rather, they are recalculated only whenever an item is changed (in which case the formula is recalculated just for that specific item), or whenever the column formula is changed (in which case the formula is recalculated for all items).
(As a side note, this is the reason why in SharePoint 2010 you cannot create or change a calculated column on a list that has more than the list view threshold of 5000 items; it would require a mass update of values in all those items, which could impact database performance.)
Thus, in order for calculated columns to accurately store "volatile" values like "Me" and "Today", SharePoint would need to somehow constantly recalculate those column values and continuously update the column values in the database. This simply isn't possible.
Alternatives to Calculated Columns
I suggest taking a different approach entirely instead of using a calculated column for this purpose.
- Conditional Formatting: You can apply conditional formatting to highlight records that meet certain criteria. This can be done using SharePoint Designer or HTML/JavaScript.
- Filtered List views: Since views of lists are queried and generated in real time, you can use volatile values in list view filters. You can set up a list view web part that only shows items where
Created is equal to [Today]. Since you can place multiple list view web parts on one page, you could have one section for today's items, and another web part for all the other items, giving you a visual separation.
- A workflow, timer job, or scheduled task: You can use a repeating process to set the value of a normal (non-calculated) column on a daily basis. You need to be careful with this approach to ensure good performance; you wouldn't want it to query for and update every item in the list if the list has surpassed the list view threshold, for example.