This entirely depends on two factors:

What the insurance covers.

What the likelyhood of actually utilizing the insurance to the full dollar amount.

Now let's look at what AppleCare gives you:

Extended phone support from 90-days to 3 years (2 years for an iPhone, iPod Touch, or iPad)

Extended hardware coverage from 1 year to 3 years (2 years for an iPhone, iPod Touch, or iPad)

What it covers is any manufacturing defect. It also covers you for phone support, as otherwise it's a $49-per-incident charge even for simple issues. It also covers any software issues that you may come across as long as the issues pertain to Apple software or the operating system itself.

What it doesn't cover is any damage caused by the user. If you snap the corner of the screen, drop it, spill liquid on it, modify it, etc... then you're responsible for paying the repair costs. If you're outside of phone support, then you're going to have to pay someone to fix any problems you come across.

Now if we're to trust this handy study done in 2009, then we can say that the 3-year failure rate for Macbooks and Macbook Pros is 17.4%.

We could go ahead and say that $350 / $2000 = 17.5% so the chances match up, but what's the likelihood that Apple is going to cover the full $2000? Only under extreme cases are you losing the full $2000 (theft, shock damage, etc...), and those are all cases that Apple won't cover anyways.

Instead we're looking at cases such as (Please keep in mind it has been several years since I worked for Apple, so these figures may be off):

A failed hard drive (est. $150-$200 for Apple to fix)

Failed memory (est. $200-$250 for Apple to fix)

A failed logic board (Est. $500-800 for Apple to fix)

So this reduces our possible savings significantly. Let's then also look at what the warranty becomes after they fixed a part:

A replacement part or Apple Product, including a user-installable part that has been installed in accordance with instructions provided by Apple, assumes the remaining term of the Warranty or ninety (90) days from the date of replacement or repair, whichever provides longer coverage for you.

Which means in this case that you have a 90-day warranty after they've fixed an issue. This significantly reduces the likelihood of a same part going bad multiple times in a row.

Therefore the chances of that $350 being worthwhile are very much against you. Even if the system does fail in some way, it is likely that the repair would be cheaper than the AppleCare. The chances of running into a repair or series of repairs that pays for the AppleCare and then some are astonishingly low.

I would still get it if you were giving it to someone who was significantly lacking in any technology concepts (such as a parent or grandparent) as they are more likely to utilize the extended phone support, especially for smaller things that they might nag you about!