Should I indicate my career plans (if any) in my personal statement?

This will hugely depend on the subject and university you are applying to. If you are applying for Medicine, I guess you can omit that since it will be quite obvious(!). In my case, I did mention some of the career paths I may possibly choose, but it was quite ambiguous and I more or less extrapolated it from my interests. Also, universities will not assume that you already have a career plan and I can honestly tell you many university students don't have one. My advice is, if you really have a specific career you want to pursue, state it and briefly link it to the subject you are applying to (e.g. skills, knowledge, etc.). Also, if you are intending to apply to a broad subject (e.g. Law, Business / Management, Natural Sciences, Engineering (general), etc.), do state some specific jobs that you might be interested in.