Well, there are some cases you must use them, like when you need to join to the same table twice in one query.
It also depends on wether you have unique column names across tables. In our legacy database we have 3-letter prefixes for all columns, stemming from an abbreviated form from the table, simply because one ancient database system we were once compatible with didn't support table aliases all that well.
If you have column names that occur in more than one table, specifying the table name as part of the column reference is a must, and thus a table alias will allow for a shorter syntax.