Why does Dijkstra hate Geralt?
In The Witcher 3 you meet an influential spy called Sigi Reuven.
Having not played previous games at all, and noticing their mutual hatred for one another, what exactly has Geralt done to Dijkstra in the past for them to hate each other's company?
Beware for Spoilers if you want to read the books!
I believe the reason Dijkstra hates Geralt goes beyond the games. The games are based on a series of books and they meet each other a few times throughout. One of the times, and I think this is the one the other answer is referring to, is when the entire Chapter coup is taking place (Sorcerers and Sorceresses betraying each other, general political plot). Dijkstra captures Geralt and takes him with him away from Ciri against his will, Geralt breaks free and in the process breaks Dijkstra's ankle/leg which causes Dijkstra to use a cane for quite a while and eventually a brace.
Dijkstra in return is a spy and later deliberately makes sure Geralt gets 'wrong' information, etc. So it's a bit of a circle. They're both doing their jobs.
Hate is also a pretty big word. The Witcher series contains a lot of political intrigue and plots, naturally that creates friction between Geralt, who wants to stay out of it all, and anyone who wants to drag him into it and (try to) manipulate him. I believe Geralt and Dijkstra didn't like each other but had a certain mutual respect for each of their jobs (in what little capacity you can have respect for spies and Witchers). They probably see each other as necessary evils.
The Witcher 3 has an impressive journal with entries for all the main characters. In the entry for Dijkstra, it is mentioned that Geralt broke Dijkstra's leg in an earlier meeting. They have also had a number of earlier meetings according to the journal entry.
If you explore all the conversation optons with Dijkstra he will mention that Geralt broke his leg the last time they met and that he must now soak it in a bath several times a day. You can also see that is wearing a metal leg brace.