This is just a quick snap shot of what I am currently using - there are probably more lurking in the multiple bags I own but I couldn't be bothered to dig them all out.
I suffer from very dry skin on my hands- see that stack of copier paper at the office? I only need to look at them before getting an instant paper cut on my dry hands. Up until earlier this month I was still wearing leather gloves on my commute to work to protect my hands from the cold weather. I hate nothing more than the feeling of sore, dry, rough skin and cannot wait to smother a healing moisturising lotion to calm and soothe my skin.
As a consequence I suffer from hangnails too and always get caught out when they snag so I find myself unladylike trying to nibble them off... A great product that helps sort out my cuticles is by OPI Avoplex Nail and Cuticle Replenishing Oil. Brush onto the cuticles before bedtime - the next day the pesky hangnails and dryness are banished.
NB: All products were bought with my own money and my opinions are my own.