What column data type should I use for storing large amounts of text or html

You should use TEXT like the others said, but there is some important advice every time you use TEXT or BLOB: decouple them form your base table as they really slow down accessing the table. Imagine the following structure:

CREATE TABLE article (
    id INT(10) UNSIGNED,
    title VARCHAR(40),
    author_id INT(10) UNSIGNED,
    created DATETIME,
    modified DATETIME
);

CREATE TABLE article_body (
    id INT(10) UNSIGNED,
    body TEXT
);

Whenever you list articles you can use the article table (last 5 articles of author 33):

SELECT id, title FROM article WHERE author_id=33 ORDER BY created DESC LIMIT 5

And when someone really opens the article you can use something like:

SELECT a.title, ab.body
FROM article AS a
   LEFT JOIN article_body AS ab ON ab.id = a.id
WHERE a.id=82

Yes, it will be better if you can store the values in the "TEXT" data type. For more details, please read this article.

Regarding knowledge of storage requirements, you can read this one.

Hope it helps.

You should be using a file, not a database to store this. Especially not MySQL. I made a writeup once explaining what happens if you for example download images out of a database BLOB, see http://mysqldump.azundris.com/archives/36-Serving-Images-From-A-Database.html. Using files, you can use the web server fast path using the sendfile(2) system call, and it is much faster to use this.

MySQL also has no BLOB API. That means, it is impossible to upload or download objects larger than max_allowed_packet, and it is hard to work your way around that using SUBSTRING(), because that will make needless copies of strings in server memory.

If you absolutely MUST store BLOB or TEXT data in the server, you have the choice of TINYTEXT, TEXT, MEDIUMTEXT and LARGETEXT which are limited to 255, 65535, 16 MB and 4GB of data in the server, additionally constrained by max_allowed_packet.

Large BLOB or TEXT information will completely wreck data density in your table. It is useful to create an artificial 1:1 or 1:0 relationship to a BLOB table, and then store the blobs in this extra table.

When MySQL shows a query plan that is 'using tempoary', it means that the server needs to materialize the result set table in the server before delivering the result. This is being done using MEMORY tables, if possible. Any TEXT or BLOB type cannot be represented in MEMORY tables, hence the temporary table then hits the disk as a MyISAM table instead.

You need to scan for such query plans, and convert them into something that loads the ID values of the BLOB/TEXT values instead. In a second query, you'd then SELECT id, thetext FROM texttable WHERE id in ( ... ) to get the TEXT/BLOB values. That will make the query with 'using temporary' not use TEXT or BLOB types, and you can get the TEXT fields then with a trivial query that runs without 'using temporary'.

You can learn more about the internals of MySQL TEXT and BLOB storage by reading http://www.mysqlperformanceblog.com/2010/02/09/blob-storage-in-innodb/

I would use text for columns with variable length.

I am here after get stuck in my development.
In my website:
I used TEXT datatype in MYSQL to store the content of the textarea given by user input. Today I give a large text (112KB) in the textarea to store in DB. and it breaks.
Then I read from internet -

TINYTEXT: 255 characters - 255 B
TEXT: 65,535 characters - 64 KB
MEDIUMTEXT: 16,777,215 - 16 MB
LONGTEXT: 4,294,967,295 characters - 4 GB

For me I have to switch to the MEDIUMTEXT.