In SQL Server 2000, if you want to identify corrupt pages, then the database option TORN_PAGE_DETECTION should be set to TRUE.
But in SQL 2005 and up, a new setting PAGE_VERIFY replaced the old TORN_PAGE_DETECTION which allows to choose from two different types of page verification : TORN_PAGE_DETECTION and CHECKSUM.
Now the question comes which one to set - TORN_PAGE_DETECTION or CHECKSUM ?
TORN_PAGE_DETECTION - writes a bit for every 512 bytes in a page allowing you to detect when a page was not successfully written to disk. The catch is that it wont tell you if the data stored in those 512 byes is actually correct or not due to the fact that couple of bytes may have been written incorrectly.
CHECKSUM - will caluclate a checksum of the page both when a page is written and when a page is read, assuming it has checksum on it.
The SQL Server computes the checksum based on the bit pattern on the page, stores it in the page header and then issues an I/O to write the page. When the SQL Server reads the page, it re-computes the checksum using the same logic and then compares it with the value available in the page header. If the checksum value matches then it is assumes the page did not get corrupted during the write-read cycle.
Since the cost of computing the checksum is incurred on each page read and write, it can add to the CPU overhead and can possibly impact the throughput of your workload. Another thing to keep in mind is that the checksum is not unique for a specific bit pattern on the page. Two pages can possibly map to the same checksum value. So there is remote possibility that page corruption may go undetected.
Reference : Checksum in SQL2005
To specifically answer your questions :
I believe Checksum was introduced in SQL2005 and that upgrading or restoring a DB from a prior version would maintain it's previous page verify method. i.e. there was no implicit upgrade.
Yes CHECKSUM was introduced in SQL Server 2005 and is the DEFAULT. When you upgrade from 2000 to 2005, you have to explicitly change the database option Page Verify to use CHECKSUM.
If you restore the database already created on sql 2005 to another server running sql 2005, you dont have to set it. It will persist to what ever you have set the Page Verify option to.
I've not succeeded in researching when Torn Page Detection came in
Versions of SQL Server earlier than 7.0
Versions of SQL Server earlier than 7.0 did not provide log parity or
torn bit detection facilities. In fact, those versions can write the
same log page multiple times until the log records fill the 2-KB log
page. This can expose transactions that have successfully committed.
If the log page is being rewritten during a failure, a sector with the
committed transaction may not get rewritten properly.
Thus, TORN_PAGE_DETECTION has been around since SQL Server 7.0. Even then, the default was that it was not enabled (same link).
Note Torn page detection is not enabled by default in SQL Server 7.0. See sp_dboption for how to enable the detection on your system.
Therefore, if the database was developed against a 7.0 instance and was subsequently upgraded, it would have upgraded the with the extant PAGE VERIFY option of NONE (as @ThomasStringer noted in his answer).
Edit : 09/24/2013 To improve the answer :
Refering to my SQL Server Internal notes from SQLSkills, I found that using a page dump, you can verify if torn bit detection - TORN_PAGE_DETECTION or CHECKSUM was enabled or not :
use database_name -- change here for your database !!
dbcc traceon (3604) -- send output to screen
dbcc page (dbaalert, 1,1,0)
dbcc traceoff (3604) -- turn off the trace flag
m_tornBits : This holds either the page checksum or the bits that were displaced by the torn-page protection bits – depending on what form of page protection is turnde on for the database.
Note: I dont have any older sql server versions running. Below is confirmed from sql server 2000 and up. If you have a 7.0 or 6.5 running around, you can confirm it as well :-)