My sister (younger than me) was definitely my mother's favourite - to be honest, I only really saw it clearly when I was grown up, and was looking back at my childhood as part of therapy for depression.
It ranged from fairly minor things - for example, we had an old and dodgy immersion heater, and it was expensive to run, so dsis and I had to share the bath water. We had baths twice a week (got to love the stinky 70s), and as she was younger, dsis always went first - so she got the clean, hot water, and I got the scummy, cooler water, plus I had to clean out the bath and tidy the bathroom.
When we were younger, this didn't matter so much, because dsis had an earlier bedtime, so the upside of having the second crack at the bathwater was that I got to stay up later. But when we got older, she stayed up as late as me, so there was no upside for me, and one day, I asked my mum if my sister and I could take turns at having the first bath - so it was equal and fair - and she said No!!
A more serious example was our 18th birthday presents - I got a £20 clock radio, and dsis got a £250 oboe. And when I went to university as a mature student, and was doing vocal solos with the university philharmonic choir and orchestra (I was a music student and a singer), my mum never once came to hear me perform, even though dad did come, so all she'd have had to do was sit in the car - no effort required. And when I was being bullied at school, and was desperately unhappy, my mum did nothing about it, and brushed me off when I tried to tell her - and never once checked up to see if the bullying was still happening. She didn't notice I was depressed, to the point of having suicidal thoughts, in my mid teens, either.
If I am honest, I am still bitter about it, but I have decided there is no point in saying anything, because mum will flat-out deny any of it - and I now live at the other end of the UK, and don't see her very often. I have decided I will just be happy with my life as it is now, and will not let her impinge on it too much. When she is nice, I will be glad of it, and when she isn't, I will ignore it.