yes it is possible to recover a .zip password. I've had to do so a couple of times.
there's a thing called brute force, which basically just guesses the password using heaps of possible combinations. if you use letters only, it will go through from a to zzzzzzzzzz.... depending on how many characters you set as the limit. the more characters, the longer it would take to break it. it works exponentially.
if you only used lower case letters, for each extra letter it has, it can take 26 times longer to guess than a password with one less character. (there are 26 letters in the alphabet)
I've used a program called Advanced Archive Password Recovery. you can download a trial
here (1.5MB)
I haven't bought the full version, because I only needed it a couple of times. but it might be worth buying if you use passworded .zip files often (although most people don't)
on .zip files, it can guess millions of passwords per second. but on .rar 3.X files, it will only be around 10-20 passwords per second. because the encryption is stronger.
so you can imagine that it would take much longer to guess a .rar 3.X password