Well, it can possibly be done but you will not be alive to see it done.
The algorithms are published. Even having them and knowing which one was used (as long it is a decent one) really doesn't help much. The math to go backwards from the hashed output to the original input is just too hard for even the best computers to execute in any amount of time that matters.
The typical way cracking works is to use social engineering to guess at what the person might use as a password and try different things until you get it right. They might also just try all combinations of letter, numbers, symbols, etc. until they get the match.
The problem with that is that any decent system will detect repeat failed attempts and just lock the account. So, to have any chance, the hacker needs to obtain a copy of the database so they can run the tests outside of the system. Once the figure it out, they can then use it to break into the account(s).
The hashing algorithms are, however, sufficiently complicated that it just takes too long for it to work well, if at all, as long as you don't use abc123 as your password.
Some older hashing systems have been partially broken but it takes a lot of time with some really powerful computers (ones too expensive for all but big businesses or the government to afford) to get there.
Here is an article that talks about a common encryption technique and how long it would take to crack it:
http://www.eetimes.com/document.asp?doc_id=1279619
Here is a quote from the article:
Most breaches in passwords are due to them either being stored in plain text or simply encrypted but the thief finds the encryption key and is able to decrypt them. Hashes, on the other hand, don't have such a key. They are just not practically reversible to get the original password.