Okay, let's look at real figures:
A single Nvidia 9800GTX can calculate 350 million MD5 hashes / second. At this rate, the entire keyspace of lower and uppercase alphanumeric characters will be done in 7 days. 7 chars, two hours. Applying salting will only double or triple these times depending on your algorithm.
Cheap modern GPUs will easily boast one billion MD5 hashes / second. Determined people typically link up about 6 of these, and get 6 billion / second, rendering the 9 character keyspace obsolete in 26 days.
Note that I'm talking about brute force here, as preimage attacks may or may not apply after this level of complexity.
Now if you want to defend against professional attackers, there is no reason they can't get 1 trillion hashes / second, they'd just use specialized hardware or a farm of some cheap GPU machines, whichever is cheaper.
And boom, your 10 character keyspace is done in 9.7 days, but then 11 character passwords take 602 days. Notice that at this point, adding 10 or 20 special characters to the allowed character list will only bring the cracking time of a 10 character keyspace to 43 or 159 days, respectively.
See the problem with password hashing is that it only reduces time until your futile doom. If you want something really strong, but still as naive as stored hashed passwords are, go for PBKDF2.
Then there is still one more problem, will the user use this "strong" password you forced him to use on all his other sites? If he doesn't save them in a master password file, he most certainly will. And those other sites wont use the same strong hashing algorithms you use, defeating the purpose of your system. I can't really see why you want your hashes to be super strong if it isn't to stop users from using the same password on multiple sites; if an attacker has access to your hashes, you most likely already lost.
On the other hand, like I will repeat and repeat again to people asking questions about how "secure" their hashing scheme is, just use client certificates, and all your problems are solved. It becomes impossible for users to use the same credentials on multiple sites, attackers cannot break your credentials without modifying them, users cannot easily have their credentials stolen if they store them on a smart card, etc etc.
To naively answer your question: a strong password is only backed by a strong hashing algorithm.