Yes, you read it correct. It is possible to jailbreak your phone without cydia. I wanted to jailbreak my iphone and never wanted to install Cydia because Cydia takes space on iphone which may create problem for those who have 8GB iphone. Generally after jailbreak iOS 5.1.1, 8gb iphone gives error of "DISK SPACE Full". To avoid this error, I jailbroke my iphone without installing Cydia. I searched a lot on internet, but there was no solution. So, I thought of an experiment. I downloaded latest Redsn0w and during Jailbreak, I unchecked the option "install Cydia". and That's it. My iphone was jailbroken. But now the problems I faced were 1. I was not able to install any .deb file 2. I was not able to install .ipa file.
If you need to access the file system of iphone only, then jailbreaking can be useful. Otherwise, to install .deb file, you need Cydia and to install IPA files, you need AppSynce which is again a .deb file.
Jailbreaking without Cydia is possible, but without Cydia, you won't be able to do much with your jailbroken iphone.