I just cannot find Cronbach's index in SPSS. Could you tell me how I can obtain the index?

Should be under Reliability Analysis....

I did it with "reliability index". Is this the same as Cronbach's alpha??? It does not say so; so I thought mayber it was based on something else. So, it is the same! Another question is that: I have a questionnaire that measures perceptions and deals with several domains, adherence, control, severity, etc. I should not put all the variables into it and then hit "reliability index". Should I choose one domain with related variables at a time? Because I get a really low index when I put all, but when I put a domain at a time, I get a high index.

This is all highly dependent on the nature of your study and what the objectives are - it sounds like you're just arbitrarily pulling stuff out / putting stuff in until you get a "good" statistic.

Therefore, I'm going to refrain from commenting on this.

Cronbach's alpha is under Analyze > Scale > Reliability Analysis in SPSS 13, then in the "Statistics" button, check "Scale" and you will get the alpha.