To be perfectly cliché, I like to believe that “things happen for a reason,” that there might be an order to the universe (can an order be secular?), and that sometimes good things can even happen to good people. These ideas deal more in the vein of positive events; I do not subscribe to inane drivel, religious or secular, that scapegoats minorities for natural disasters, the breakdown of family values, etc.My response to karma will be similar to my response to faith. That is, it depends what kind of karma we're talking about here.
There are, after all, at least a few concepts of karma which I consider to be nonsense. For instance, in some traditions, karma carries over through reincarnation, from life to life. Therefore, someone who was good and holy and practiced the right rituals at the right times would in his next life be reborn in one of the upper castes, while someone who was evil and greedy and disrespectful to the gods would be reborn in one of the lower castes, if any caste at all. And that's why poor people deserve their poverty.
Besides being premised on the belief in reincarnation, and lacking any sort of evidence (how do we know it isn't the other way around, with good people being born into lower castes?), it also seems exceptionally unjust. I don't think I should be held responsible for actions in past lives just because those past lives share some unfathomable soulstuff with my own. It seems to me the whole motivation for karma is the idea of justice (rather than the idea of evidence), and this particular kind of karma can't even get justice right.
Another example of karma which I think rather silly is the Jainist concept that karma comes in small particles. These karmic particles stick to your soul, and have complex (but apparently understood to very fine detail) interactions which influence how you think, how you feel, and what happens to you. This belief seems far more specific and extraordinary than we have evidence to justify.
But of course, people are free to pick and choose the kinds of karma which are not so egregiously wrong. The questioner on Friendly Atheist, for instance, believes in karma, meaning "good things can even happen to good people". I note that he left out the part about bad things happening to bad people, which seems equally reasonable, but let us not dwell on it. This kind of karma, of course, is completely correct. Good things can happen to good people. I've seen it with my own eyes! I might go even so far as to suggest that, sometimes, good things happen to good people because they are good. Isn't that quite amazing and wonderful?
However--and don't let this subtract from any earlier feeling of amazingness and wonderfulness--I'd say that this occurs by completely natural mechanisms which you are probably already familiar with. For example, when you are nice to people, they tend to be nice back. When you break the law, that increases your chance of getting caught from zero to nonzero. If you work hard on your homework, you may occasionally learn something which will help you later. And if you pray to the gods, then you might... then you might...
Okay, so it doesn't always work. We can't always find a mechanism which links good actions to good consequences and bad actions to bad consequences. It might be, of course, that we were mistaken about which actions and consequences were good and bad, but then it might be the case that karma is simply incorrect in these cases. If we can't think of some reasonable mechanism, perhaps that's because there isn't one.
You might ask, what if there's a mechanism and I'm simply not aware of it? That is always a possibility. But it seems equally possible that there's a mechanism which links good deeds with bad consequences and vice versa. Perhaps, in these particular circumstances, the world operates under the principle of "no good deed goes unpunished" rather than the principle of karma. And since we don't have any clue as to the mechanism, how do we know what these "particular circumstances" are? Maybe it only works on Tuesdays, and backfires on Thursdays? Maybe it only works if your name begins with a B? Or maybe it depends on whether a particular butterfly in Australia flapped its wings on May 3rd, at exactly quarter to four in the afternoon. And so the argument from "you don't know either" fails again.
But perhaps I dwell too much on the incorrect concepts of karma (since they are the most deserving of criticism). Let's not forget that sometimes karma is correct, that sometimes good things happen even to good people. Let's not forget how amazing and wonderful that is.
I suggest that it would still be wonderful and amazing even if we didn't call it karma. The word karma suggests some single mechanism, when really there are a collection of mechanisms which causally link good deeds to good results. The word karma also has the unfortunate association with the caste society in India. It's worth thinking about, but don't let that stop you from using words as you see fit.