The Stalker Series is pretty good imo, I would install the complete mod with it. The complete mod improves AI, graphics, sound, fixes bugs, but leaves the game close to vanilla.
Stalker is open world fps/rpg hybrid with survival horror elements. It also takes place around the Chernobyl erea so it has a similar eastern european asthetic to DayZ. I think the stalker environments are more detailed and interesting than DayZ's.
It is a little more story oriented and has an open level design, you have to eat food or starve, sleep or pass out unconcious possibly in a dangerous area, scavange for supplies, find and upgrade equipment, equipment degrades so you have to repair, guns jam on you, there are blowouts that you have to take shelter from or die. There is radiation, bandages to stop bleeding, blood leaves tracks, so you can track enemies or be tracked by enemies. You have to avoid anomolies which can also kill you. The environment is very dangerous.
Fallout New Vegas but only on Hardcore mode has more of a survival element to it as well.
Both are single player, and both are more open world, like DayZ.
There is an indie title that is a zombie survival game that is unfinished, it's not fps and has oldschool 2d graphics. It is currently in development put is playable if you preorder. It is called Project Zomboid. You hunt down materials to build barriers on doors and windows, you get hungry, cold, sleepy, sick, and you have to scavange the surrounding area for supplies.
Thats all I can think of off the top of my head.
If anyone else knows of some similar games I'd like to hear suggestions as well.