The short answer is YES, PDO prepares are secure enough if used properly.
I'm adapting this answer to talk about PDO...
The long answer isn't so easy. It's based off an attack demonstrated here.
The Attack
So, let's start off by showing the attack...
$pdo->query('SET NAMES gbk');
$var = "\xbf\x27 OR 1=1 /*";
$query = 'SELECT * FROM test WHERE name = ? LIMIT 1';
$stmt = $pdo->prepare($query);
$stmt->execute(array($var));
In certain circumstances, that will return more than 1 row. Let's dissect what's going on here:
- Selecting a Character Set - $pdo->query('SET NAMES gbk');
 - For this attack to work, we need the encoding that the server's expecting on the connection both to encode - 'as in ASCII i.e.- 0x27and to have some character whose final byte is an ASCII- \i.e.- 0x5c.  As it turns out, there are 5 such encodings supported in MySQL 5.6 by default:- big5,- cp932,- gb2312,- gbkand- sjis.  We'll select- gbkhere.
 - Now, it's very important to note the use of - SET NAMEShere. This sets the character set ON THE SERVER. There is another way of doing it, but we'll get there soon enough.
 
- The Payload - The payload we're going to use for this injection starts with the byte sequence - 0xbf27.  In- gbk, that's an invalid multibyte character; in- latin1, it's the string- ¿'.  Note that in- latin1and- gbk,- 0x27on its own is a literal- 'character.
 - We have chosen this payload because, if we called - addslashes()on it, we'd insert an ASCII- \i.e.- 0x5c, before the- 'character. So we'd wind up with- 0xbf5c27, which in- gbkis a two character sequence:- 0xbf5cfollowed by- 0x27. Or in other words, a valid character followed by an unescaped- '. But we're not using- addslashes(). So on to the next step...
 
- $stmt->execute() - The important thing to realize here is that PDO by default does NOT do true prepared statements. It emulates them (for MySQL). Therefore, PDO internally builds the query string, calling - mysql_real_escape_string()(the MySQL C API function) on each bound string value.
 - The C API call to - mysql_real_escape_string()differs from- addslashes()in that it knows the connection character set. So it can perform the escaping properly for the character set that the server is expecting. However, up to this point, the client thinks that we're still using- latin1for the connection, because we never told it otherwise. We did tell the server we're using- gbk, but the client still thinks it's- latin1.
 - Therefore the call to - mysql_real_escape_string()inserts the backslash, and we have a free hanging- 'character in our "escaped" content! In fact, if we were to look at- $varin the- gbkcharacter set, we'd see:
 - 縗' OR 1=1 /* - Which is exactly what the attack requires. 
- The Query - This part is just a formality, but here's the rendered query: - SELECT * FROM test WHERE name = '縗' OR 1=1 /*' LIMIT 1
 
Congratulations, you just successfully attacked a program using PDO Prepared Statements...
The Simple Fix
Now, it's worth noting that you can prevent this by disabling emulated prepared statements:
$pdo->setAttribute(PDO::ATTR_EMULATE_PREPARES, false);
This will usually result in a true prepared statement (i.e. the data being sent over in a separate packet from the query). However, be aware that PDO will silently fallback to emulating statements that MySQL can't prepare natively: those that it can are listed in the manual, but beware to select the appropriate server version).
The Correct Fix
The problem here is that we used SET NAMES instead of C API's mysql_set_charset(). Otherwise, the attack would not succeed. But the worst part is that PDO didn't expose the C API for mysql_set_charset() until 5.3.6, so in prior versions it cannot prevent this attack for every possible command!
It's now exposed as a DSN parameter, which should be used instead of SET NAMES...
This is provided we are using a MySQL release since 2006. If you're using an earlier MySQL release, then a bug in mysql_real_escape_string() meant that invalid multibyte characters such as those in our payload were treated as single bytes for escaping purposes even if the client had been correctly informed of the connection encoding and so this attack would still succeed.  The bug was fixed in MySQL 4.1.20, 5.0.22 and 5.1.11.
The Saving Grace
As we said at the outset, for this attack to work the database connection must be encoded using a vulnerable character set.  utf8mb4 is not vulnerable and yet can support every Unicode character: so you could elect to use that instead—but it has only been available since MySQL 5.5.3.  An alternative is utf8, which is also not vulnerable and can support the whole of the Unicode Basic Multilingual Plane.
Alternatively, you can enable the NO_BACKSLASH_ESCAPES SQL mode, which (amongst other things) alters the operation of mysql_real_escape_string().  With this mode enabled, 0x27 will be replaced with 0x2727 rather than 0x5c27 and thus the escaping process cannot create valid characters in any of the vulnerable encodings where they did not exist previously (i.e. 0xbf27 is still 0xbf27 etc.)—so the server will still reject the string as invalid.  However, see @eggyal's answer for a different vulnerability that can arise from using this SQL mode (albeit not with PDO).
Safe Examples
The following examples are safe:
mysql_query('SET NAMES utf8');
$var = mysql_real_escape_string("\xbf\x27 OR 1=1 /*");
mysql_query("SELECT * FROM test WHERE name = '$var' LIMIT 1");
Because the server's expecting utf8...
mysql_set_charset('gbk');
$var = mysql_real_escape_string("\xbf\x27 OR 1=1 /*");
mysql_query("SELECT * FROM test WHERE name = '$var' LIMIT 1");
Because we've properly set the character set so the client and the server match.
$pdo->setAttribute(PDO::ATTR_EMULATE_PREPARES, false);
$pdo->query('SET NAMES gbk');
$stmt = $pdo->prepare('SELECT * FROM test WHERE name = ? LIMIT 1');
$stmt->execute(array("\xbf\x27 OR 1=1 /*"));
Because we've turned off emulated prepared statements.
$pdo = new PDO('mysql:host=localhost;dbname=testdb;charset=gbk', $user, $password);
$stmt = $pdo->prepare('SELECT * FROM test WHERE name = ? LIMIT 1');
$stmt->execute(array("\xbf\x27 OR 1=1 /*"));
Because we've set the character set properly.
$mysqli->query('SET NAMES gbk');
$stmt = $mysqli->prepare('SELECT * FROM test WHERE name = ? LIMIT 1');
$param = "\xbf\x27 OR 1=1 /*";
$stmt->bind_param('s', $param);
$stmt->execute();
Because MySQLi does true prepared statements all the time.
Wrapping Up
If you:
- Use Modern Versions of MySQL (late 5.1, all 5.5, 5.6, etc) AND PDO's DSN charset parameter (in PHP ≥ 5.3.6)
OR
- Don't use a vulnerable character set for connection encoding (you only use utf8/latin1/ascii/ etc)
OR
- Enable NO_BACKSLASH_ESCAPESSQL mode
You're 100% safe.
Otherwise, you're vulnerable even though you're using PDO Prepared Statements...
Addendum
I've been slowly working on a patch to change the default to not emulate prepares for a future version of PHP. The problem that I'm running into is that a LOT of tests break when I do that. One problem is that emulated prepares will only throw syntax errors on execute, but true prepares will throw errors on prepare. So that can cause issues (and is part of the reason tests are borking).