Is there a lot of value in learning to write Chinese characters? I have noticed that a lot of my friends that study Chinese at university spend a lot of their time learning to write Chinese. I would estimate more than 50% of their Chinese study time is spent on memorizing how to write Chinese characters.

I'm considering studying Chinese at university, but I'm unsure because I would have to learn to write, which I feel would be a big investment of my time which could be spent  practicing reading, listening and speaking.

Even with English, I feel I hardly ever write anything with a pen. Everything is done on cell phones, computers, etc. now and I feel this trend is only going to continue. 

So, is there a value in learning to write characters by hand, if I know how to write them via pinyin input? Or should I continue to focus my time on learning to read, speak and listen instead?
You're right that most of the time, you use a computer or cell phone when "writing" Chinese characters. In fact, many Chinese will tell you that - beside their own name (used as a signature) - they almost never write any Chinese characters by hand.

Today, writing Chinese characters is more for memorization than for practical purposes. You might know a few characters and you might know how to type them in your computer, but the only way to really keep them in your mind, and being able to read them fluently, is to write them. It is however rather tedious so it works better if you have some interest in Chinese characters to begin with, otherwise it might get boring.

The best way might be to just try. Write a few characters every day and you might find yourself interested in all the subtleties of Chinese characters.

Edit: There's a related question about the relation between writing and memorizing on the Cognitive Sciences Stack Exchange - https://cogsci.stackexchange.com/q/68/63