I think Data is incapable (outside of unique situations like Lore or Q's tampering) of feeling base emotions: anger, fear, sadness, joy, surprise, disgust
Except at the end of The Most Toys he fires the disruptor at Fajo, an action of anger. (Unless you really want to believe what he said about it maybe being triggered by the transporter, which was ridiculous because if the transporter could make a weapon discharge everyone would shoot their balls off with their own phasers whenever they beam anywhere)
Except he has a self-preservation instinct that makes him try to avoid unnecessary danger and damage, which is all fear really is.
Except he can feel loss, the lack of someone he cared for (Tasha Yar, Lal). That's why he had to download Lal's memories at the end of Offspring, and why he kept the picture of Tasha (which he had no other reason for keeping; it's not like Data is capable of ever forgetting what someone looks like). Isn't missing someone's company, or the way they enriched your life, one of the greatest forms of sadness?
Surprise definitely isn't a base emotion, but Data shows that pretty much every time something bizarre happens.
Now, I fully believe Data *believes* he doesn't feel emotions, and that he feels them differently, in a much more muted and less all-consuming manner than most humans. It's like the difference between a placid lake and a raging river. Just because you can't hear the lake roaring like the river, just because it's still and won't bash you against rocks if you jump in, those things don't make it stop being water.
In the end, though, it seems like the writers of the show wanted to leave it intentionally open to interpretation. So annoying, lol.