A car with the possbility of 4WD next to 2WD will certainly be heavier, resulting in higher taxes, higher fuel consumption etc. 4WD itself is also more fuel consuming. On the other hand, you'll have better driveability, especially in bad weather or in the mountains, or when driving through mud/sand/grass etc.
But it's also another thing in your car that can break. Sounds weird, but what you don't have can't get broken. For example, the Mitsubishi Outlander 2004 was also available in 2WD only version, and in 4WD.(where you could switch between 2WD and 4WD) I have two familymembers, one had the 2WD, the other had the 4WD. The 4WD was designed after the 2WD, but it wasn't properly rebuild for that. For example, it had the same clutch. This among other things formed a problem. It was prone to failure because it wasn't designed to cope with the load of 4WD. The clutch always broke when applying a fair load in 4WD modus. I'd recommend you to google for these kind of stories for the Honda CRV.