A lot of canonites think that the First Officer is equivalent to the Navy's Executive Officer billet. No, not really.
Starfleet is, in fact, a commercial airline that can trace its roots all the way back to 20th century Earth's Pan-Am. Thus it is appropriate to consider the non-flying pilot the "first officer." And except for one or two occasions, how often did Spock fly? And how else can you explain the elevation of an evident mutineer to the XO spot? Yeah, that's what I thought.
It is also crucial to recall that Landru was a commercial pilot and avid Horatio Hornblower fan. By keeping this in mind, then the apparently silly rank structure of Starfleet makes perfect sense. Get with the program and become One with the Body, sport.
Duties and Responsibilities
Everything cool the Captain gets to do, which is everything under the sun in the realm sci-fi adventure, you get to do with none (read: NONE) of the attached responsibilities. You get full access to the armory, the ability to fly any Shuttlecraft and support ships at any time for whatever reason you feel like making up, high-level security clearance, a bigger paycheck than 98% of your coworkers, better quarters, and free reign on your ship/base. Not to mention the the fact you get to boss around everyone except your commanding officer, chief medical officer, and the odd visiting Admiral or diplomat. But what are the things expected of you as first officer?
All you have to do is walk onto the bridge and stand next to the Captain for at least 15 minutes a day.
Now sometimes, you may also where a blueshirt and be asked to pull double duty as science officer. This is less a curse than a blessing. One, a blueshirt on your person makes you deathproof (think about it). Two, you get double pay. Three, you get to relay information from a big computer to your crew - which really is remarkably simple but everyone will think you're just the smartest goddamn brain around for essentially expressing verbally all the stuff the supercomputer/sensor network has already scanned and calculated. And you get a nifty free tricorder to top it all off.
Basically, an XO gets all sex, glory, action and adventure the Captain gets, just without any paperwork or requirement to give a damn.