Taking the ferry from Karakoy to Haydarpasa is one of the rituals I enjoy very much every time I visit Istanbul.
I stay on the Asian side, so I take the train down to Haydarpasa, have a glass of tea at the pier, take some photos of seagulls and pigeons, and then board the ferry over to Karakoy.
Depending on how much time I have, I might spend some time in Karakoy or head on up to Istiklal Caddesi via the Tunel and have some dessert at Inci (a place that mass produces chocolate profiteroles for three bucks a piece). My brother and I used to go there every chance we got, so, on this visit I had two — one for him, one for me.
On the way back to Haydarpasa, I prefer to sit on the port side again, this time facing into the Straits of Istanbul. As the ferry approaches Uskudar, the Maiden's Tower comes into view. The video on this page starts there.