When to use single quotes, double quotes, and backticks in MySQL

Backticks are to be used for table and column identifiers, but are only necessary when the identifier is a MySQL reserved keyword, or when the identifier contains whitespace characters or characters beyond a limited set (see below) It is often recommended to avoid using reserved keywords as column or table identifiers when possible, avoiding the quoting issue.

Single quotes should be used for string values like in the VALUES() list. Double quotes are supported by MySQL for string values as well, but single quotes are more widely accepted by other RDBMS, so it is a good habit to use single quotes instead of double.

MySQL also expects DATE and DATETIME literal values to be single-quoted as strings like '2001-01-01 00:00:00'. Consult the Date and Time Literals documentation for more details, in particular alternatives to using the hyphen - as a segment delimiter in date strings.

So using your example, I would double-quote the PHP string and use single quotes on the values 'val1', 'val2'. NULL is a MySQL keyword, and a special (non)-value, and is therefore unquoted.

None of these table or column identifiers are reserved words or make use of characters requiring quoting, but I've quoted them anyway with backticks (more on this later...).

Functions native to the RDBMS (for example, NOW() in MySQL) should not be quoted, although their arguments are subject to the same string or identifier quoting rules already mentioned.

Backtick (`)
table & column ───────┬─────┬──┬──┬──┬────┬──┬────┬──┬────┬──┬───────┐
                      ↓     ↓  ↓  ↓  ↓    ↓  ↓    ↓  ↓    ↓  ↓       ↓
$query = "INSERT INTO `table` (`id`, `col1`, `col2`, `date`, `updated`) 
                       VALUES (NULL, 'val1', 'val2', '2001-01-01', NOW())";
                               ↑↑↑↑  ↑    ↑  ↑    ↑  ↑          ↑  ↑↑↑↑↑ 
Unquoted keyword          ─────┴┴┴┘  │    │  │    │  │          │  │││││
Single-quoted (') strings ───────────┴────┴──┴────┘  │          │  │││││
Single-quoted (') DATE    ───────────────────────────┴──────────┘  │││││
Unquoted function         ─────────────────────────────────────────┴┴┴┴┘

Variable interpolation

The quoting patterns for variables do not change, although if you intend to interpolate the variables directly in a string, it must be double-quoted in PHP. Just make sure that you have properly escaped the variables for use in SQL. (It is recommended to use an API supporting prepared statements instead, as protection against SQL injection).

// Same thing with some variable replacements
// Here, a variable table name $table is backtick-quoted, and variables
// in the VALUES list are single-quoted 
$query = "INSERT INTO `$table` (`id`, `col1`, `col2`, `date`) VALUES (NULL, '$val1', '$val2', '$date')";

Prepared statements

When working with prepared statements, consult the documentation to determine whether or not the statement's placeholders must be quoted. The most popular APIs available in PHP, PDO and MySQLi, expect unquoted placeholders, as do most prepared statement APIs in other languages:

// PDO example with named parameters, unquoted
$query = "INSERT INTO `table` (`id`, `col1`, `col2`, `date`) VALUES (:id, :col1, :col2, :date)";

// MySQLi example with ? parameters, unquoted
$query = "INSERT INTO `table` (`id`, `col1`, `col2`, `date`) VALUES (?, ?, ?, ?)";

Characters requring backtick quoting in identifiers:

According to MySQL documentation, you do not need to quote (backtick) identifiers using the following character set:

ASCII: [0-9,a-z,A-Z$_] (basic Latin letters, digits 0-9, dollar, underscore)

You can use characters beyond that set as table or column identifiers, including whitespace for example, but then you must quote (backtick) them.

Also, although numbers are valid characters for identifiers, identifiers cannot consist solely of numbers. If they do they must be wrapped in backticks.

There are two types of quotes in MySQL:

' for enclosing string literals
` for enclosing identifiers such as table and column names

And then there is " which is a special case. It could be used for one of above-mentioned purposes at a time depending on MySQL server's sql_mode:

By default the " character can be used to enclose string literals just like '
In ANSI_QUOTES mode the " character can be used to enclose identifiers just like `

The following query will produce different results (or errors) depending on SQL mode:

SELECT "column" FROM table WHERE foo = "bar"

ANSI_QUOTES disabled

The query will select the string literal "column" where column foo is equal to string "bar"

ANSI_QUOTES enabled

The query will select the column column where column foo is equal to column bar

When to use what

I suggest that you avoid using " so that your code becomes independent of SQL modes
Always quote identifiers since it is a good practice (quite a few questions on SO discuss this)

(There are good answers above regarding the SQL nature of your question, but this may also be relevant if you are new to PHP.)

Perhaps it is important to mention that PHP handles single and double quoted strings differently...

Single-quoted strings are 'literals' and are pretty much WYSIWYG strings. Double-quoted strings are interpreted by PHP for possible variable-substitution (backticks in PHP are not exactly strings; they execute a command in the shell and return the result).

Examples:

$foo = "bar";
echo 'there is a $foo'; // There is a $foo
echo "there is a $foo"; // There is a bar
echo `ls -l`; // ... a directory list

Backticks are generally used to indicate an identifier and as well be safe from accidentally using the Reserved Keywords.

For example:

Use `database`;

Here the backticks will help the server to understand that the database is in fact the name of the database, not the database identifier.

Same can be done for the table names and field names. This is a very good habit if you wrap your database identifier with backticks.

Check this answer to understand more about backticks.

Now about Double quotes & Single Quotes (Michael has already mentioned that).

But, to define a value you have to use either single or double quotes. Lets see another example.

INSERT INTO `tablename` (`id, `title`) VALUES ( NULL, title1);

Here I have deliberately forgotten to wrap the title1 with quotes. Now the server will take the title1 as a column name (i.e. an identifier). So, to indicate that it's a value you have to use either double or single quotes.

INSERT INTO `tablename` (`id, `title`) VALUES ( NULL, 'title1');

Now, in combination with PHP, double quotes and single quotes make your query writing time much easier. Let's see a modified version of the query in your question.

$query = "INSERT INTO `table` (`id`, `col1`, `col2`) VALUES (NULL, '$val1', '$val2')";

Now, using double quotes in the PHP, you will make the variables $val1, and $val2 to use their values thus creating a perfectly valid query. Like

$val1 = "my value 1";
$val2 = "my value 2";
$query = "INSERT INTO `table` (`id`, `col1`, `col2`) VALUES (NULL, '$val1', '$val2')";

will make

INSERT INTO `table` (`id`, `col1`, `col2`) VALUES (NULL, 'my value 1', 'my value 2')

In MySQL, these symbols are used to delimit a query ` ," ,' and () .

" or ' are used for enclosing string-like values "26-01-2014 00:00:00" or '26-01-2014 00:00:00' . These symbols are only for strings, not aggregate functions like now, sum, or max.
` is used for enclosing table or column names, e.g. select `column_name` from `table_name` where id='2'
( and ) simply enclose parts of a query e.g. select `column_name` from `table_name` where (id='2' and gender='male') or name='rakesh' .