Penalties or bad stuff suggestions.

My experience so far suggests that people usually respond better to positive stimuli than negatives.

So if you want to encourage people to sometimes spend their resources on dealing with an event rather than focusing purely on moving towards victory, then perhaps you could try giving some significant benefit to diverting your resources that way. Perhaps if you deal with the dragon problem you might end up being the proud owner of a pile of dragon scales which might allow you some additional actions later. Or something. The "punishment" for not dealing with a problem would be that someone else might get the benefit.

Do this right and you might end up with alternate paths to victory, which has to be a good thing -- though you then need to try to balance the options, but that is a good problem to have.

But as Seph pointed out, you haven't really given enough details to allow us to give really solid advice here.

I always favoured making the punishment a little understated - and to fit the crime. I like having delayed consequences that come back to bite players 2 or 3 turns later.

For example, my game features random spawn Vikings that attack. Players can choose to ignore these Vikings, as they don't actually influence the win/loss condition much (at least right away). But then ignoring them for 2 or 3 turns often becomes disastrous as the Vikings rampage around the country side and slowly - ever so slowly - accrue the loss condition points.

I don't know how easy it is to apply to your game, but a slow burn loss condition is always "nice". Another alternative is to use something similar to the Reckoning mechanic from Eldritch Horror.

I would add as a general note to keep in mind - in my opinion it's better to have negative consequences come as a natural result, not as a rule that adds a "punishment". Example: you can invest resources in a temporary boost to an ability that gives a large, immediate advantage, or you can save your resources for a smaller, more expensive permanent boost to that ability. You may choose the temporary boost, but once it expires, the natural penalty is that you're back to normal and your resources are depleted simply from purchasing that boost. No need to add a punishment.

Alternatively, if you save up for the permanent boost, you can always count on it to be there - the downside is that in the meantime you're more vulnerable or less capable until you finally can afford the permanent boost.

Both options have pros and cons, without needing to punish anyone.

Not as such. There is nothing wrong with negative consequences, and Lew Pulsipher (who posts here pretty regularly) has talked on the tendency of modern games to heap rewards on people, rather than to punish poor play, and I am certain he is not alone in that. (I hope I'm not misrepresenting you, Lew!)

I think that the issue is that when most people play games they like to come away with positive feelings, so losing because they didn't build quite as nicely as the winner is often a better outcome than losing because they got ground into the dust by whatever forces. This possibly explains the popularity of "point salad" games like those created by Stephan Feld, where just about everything you do scores points and the contest is in trying to score most efficiently.

This doesn't apply to everyone, or every game, and there is no reason why a punishing game can't be awesome. Providing a snowballing punishment for not dealing with some challenge could be fantastic. My preference, however, would be to first look for ways to reward good play rather than punish poor, and if that didn't work out as I wanted, try the other way around.

I think the scenario you mentioned about a Kraken attacking and your decision to deal with it or not sounds like it has the "built-in" consequences I was talking about. But it does need to have a balance - if you ignore a problem like that, your other option needs to have the potential for a worthwhile reward. And I'm sure you've thought that through already.

I had the impression you were trying to add some further punishment for making certain choices. I've researched this in games that try to force a leading player to have disadvantages - not because of poor choices, but simply because they're ahead.