How to analyse 3 by 3 design with Likert scale ratings? I want to understand what would be the best way to analyze the results of an online likert-scale ratings of pictures on 3 dimensions. I have 3 groups of participants from different countries. They are not equal. I got the data into SPSS already but now I wonder what would be the appropriate way to deal with the data.
A rating scale is not necessarily a Likert scale.  It sounds like you have a single rating for each picture across each dimension but I could be wrong.  More details would be needed for better advice and Ana's comment should be answered in your question.

You would be best off doing a multi-level cumulative link model (multi-level ordinal regression).  You can include subject and picture as random variables.  See the ordinal package in R.  The vignettes will be very helpful.  

Keep in mind that with the pictures you also have item level variance and generalization issues that people doing research on words struggle with as well.  Even if you can get reasonably good looking data for your analysis that satisfies an ANOVA you'll have to consider random and fixed effects issues of both the people and the pictures.  The multi-level modelling can include both and avoid the sort of patchwork hoops required with ANOVA.  Therefore, regardless of whether you have a true likert scale and you satisfy requirements for treating the responses continuously or you should be treating it as ordinal data, multi-level modelling is your best bet.