I like to refer to this ship as the obvious one. Jack is the first person we see Kate interact with. He helps her overcome her fears and it's obvious that Kate feels a link between them. Despite their different lifestyles and past, Kate and Jack obviously click and almost appear to be soulmates. Jack is the first one to find out about Kate's dark past and at first is ready to accept it but his trust issues are getting bigger and bigger which leads to conflicts between those two. But in the end they are always there to help each other. Despite their issues, there's just a certain connection between them and they both can't deny it.

Sawyer obviously has the hots for Kate. That said, Kate seems to be fighting a connection between them, maybe even an attraction. She is the only one reaching through to him and kind of is able to control him or cool him down. Sawyer went through getting turtored in order to get a kiss from Kate which she might have or might have not liked. It seems being with Kate brings out a better side in Sawyer. She's the only one knowing of his shady past.

Kate's connection with Charlie is more based on friendship than romance. They do seem to be good friends though, bonding in the first two episodes while they were on the search for the cockpit and the transceiver. Kate was horrified when they found Charlie dead and when Jack couldn't revive him she was full of grief. But luckily Jack in the end was able to revive him nonetheless and Kate and Charlie appear to be good friends.

As with Charlie I believe the relationship between Kate and Sayid is also based on friendship. Kate was worried about Sayid when he took off into the jungle - she obviously trusts him and cares about him, though as a friend and not a potential love interest.