Short answer: Any relational database is going to read in the entire row when you select it. You will save network traffic and probably space in some internal buffers only.
Longer answer: Any relational database will read the entire page the row resides on when you select a row.
This means that tables with more columns will have less efficient pages which will need to be read/buffered more frequently per row.
This also means there is an exception: columns that are stored in overflow pages away from the rest of the row like blob or text columns or (in some db's) very long varchars may not necessarily be read if you don't select them.
There is an additional, very important exception: if you use a covering index then the db will not need to read the data page the row resides on. For example, if you have an index on (username, user_id) and you select "select user_id from table where username=xxxxx" then it will be able to read the user_id from the leaf node of the index and no bookmark lookup to the data pages will be needed. In some db's the primary key is always "covered" and you never need a bookmark lookup to get it.
Longer answer: Any relational database will read the entire page the row resides on when you select a row.
This means that tables with more columns will have less efficient pages which will need to be read/buffered more frequently per row.
This also means there is an exception: columns that are stored in overflow pages away from the rest of the row like blob or text columns or (in some db's) very long varchars may not necessarily be read if you don't select them.
There is an additional, very important exception: if you use a covering index then the db will not need to read the data page the row resides on. For example, if you have an index on (username, user_id) and you select "select user_id from table where username=xxxxx" then it will be able to read the user_id from the leaf node of the index and no bookmark lookup to the data pages will be needed. In some db's the primary key is always "covered" and you never need a bookmark lookup to get it.