Yes, but it's illegal. This is how:

1) Using a keylogger installed on the victims computer to log key presses and mouse clicks. This data is then either sent to the hacker or later retrieved.

2) Using a brute-force program that would guess anywhere from hundreds to thousands of common passwords, or using dictionary words to guess.

3) (The most common) Making a good guess. For instance, my friends cracked my roommates computer login by asking him questions like, what's your favorite number (hint: it's usually close to their street address or other number they know), and others.

You must either be able to guess or have access to the users email thats the most feasible way. Or setup a phisher website. A phisher website looks just like the myspace homepage but sends the email and password typed in to your email. This is very difficult to do on Myspace now so you need to do it from another website, email or messenger.

The best way is to have your friend or person you want to hack log on your computer and hope that they click "remember me." My friend saved her log in info on my computer and boy did I have fun. I really did some damage :) But it was just all fun and games

Not without some form of password stealing/keylogging. Guessing every possible combination is not feasible as the time it would take would to great, because also, facebook would either block the account or block your IP from their server.

The same goes for myspace and any other reputable sites with logins.

cracking is the most inefficient way to get into someone's facebook or myspace.

basically, cracking is just having a program go through a list of passwords until it gets it right.

if you know their login email address, you can use a cracking program (with rotating proxy) to try and get in, but it will take forever.

The better ways have already been mentioned but here is the correct order:
1) backdoor exploit (not likely to find one on either of those sites)
2) "social engineering". basically getting them to tell you their password out right.
3) A keylogger on a machine they use to login (THIS IS PROBABLY THE EASIEST IF YOU SPEND ANY TIME WITH THE PERSON)
4) a phishing website. (terribly difficult to use now a days, with all the anti-phishing going around. if you hack their hosts file so myspace.com points to your site, it would work best. but if you're able to hack their hosts file, you could just use a keylogger)
5) One that people rarely think of: check their firefox. go to preferences/security/show passwords then click the show passwords button. It would work on me, and I'm a security prone person!