Hi Rasmus,
There are a bunch of helpdesk apps out there but it mainly comes down to personal preference and what you both need and don't need. For example, while Zendesk might be great for larger companies, smaller businesses might find Zendesk to be a bit more complicated than necessary.
Having said that, it would be helpful to get a list of what you need to engage with your customers for your business. If you're looking for a helpdesk app that enables you to engage with customers in a personal, non-robotic manner and is simple to use yet powerful and customizable, I'd suggest you gives Reamaze (us) a try (https://apps.shopify.com/reamaze). We also offer live chat as an option, and we're integrated with Shopify so you can have your customer's Shopify data at your fingertips when you communicate with them.
Again, If you have any specific features you need answers about, I'd love to help you out or point you in the right direction. We have a long list of Shopify (and other ecommerce solutions) customers that are happy with Reamaze (just check out some of their reviews on https://apps.shopify.com/reamaze)