The first time flyer -
This is probably the best type of person to sit next to on an airplane, not that it's good to sit next to anyone. They start off extremely nervous and either consciously or subconsciously falsely acknowledge that there is at least an 80% chance that the plane will crash. These people are usually quiet the whole plane trip, because they are awaiting death, unless they talk to you to calm their nerves. When we land they think it's a miracle and have a renewed faith in God. Takeoff is the best part (unless they grip your hand). Normally they tightly grip the armrest with either wide eyes or eyes tightly shut. As the plane tilts backward you can see their pulse increasing and their heart sinking. Landing is amusing as well.
The non-English speaker -
Nothing aggravates me more than when someone who doesn't speak English talks to me in their native tongue (usually Asian). Do I look like I speak * insert any language other than English and Spanish here *? These people often don't know how things work or regularly run, and some flight attendant has to make hand signals to them to show them what to do. It'd strike me as important to learn the basics of the country's language you're visiting.
The obnoxious one -
These people take it upon themselves to speak very loudly and laugh at things that are not funny. Commonly combined with the tourist and first-time flyer, these people make your already miserable flight worse, especially when they talk about how hot the pilot is, the turbulence, how successful their company is, and their preferences in the opposite sex.
Obese people -
One of the worst to get stuck sitting next to. These people crowd your already cramped space. They barely fit into their economy class seat and take up half of yours simply by putting their arm on the armrest. If you lift the armrest then their rolls will roll over onto you. Normally this pushes you into the person next to you which only makes things worse depending on what kind of person it is.
Guys that hit on the flight attendant -
They hold up the flight attendant to ask them where they're from, endlessly flirt with them, and tell them how good looking they are. I'm sitting there waiting for my nasty plastic flavored peanuts and for five minutes they babble on about their jobs and how hard they are (how hard their jobs are, heh heh). News flash bubby: as soon as this flight is over you'll never see her again. Oh you go her number? That's great, good luck trying to call her when she's 40,000 feet in the air traveling at the speed of sound six days a week moron, in between her other calls, which will inevitably be her family and the other guys she's given her number to.
The most annoying little things to burden this godforsaken tube. They don't stop crying. I can hear them over the engines. It's an incessant crying, probably because their ear hurts or something. The parents hardly ever do anything to fix it too. They just let them cry like they'll stop soon, but naturally they don't.
These are babies that can talk, so basically now you know what the problem is, but the parents still don't do anything to fix it. If they have siblings you can multiply the chaos by at least four, and they will usually argue. Plus, when one's ear starts to hurt, so does the other's, whether it really does or not; they just want attention. When they run down the aisle is particularly annoying.
Tall people -
They block your view of the in-flight movie (which usually sucks anyway).
Stinky people -
You'd dislike these people at any time, but now they're worse because of the enclosed and cramped spaces.
Unavoidable. Almost 100% of the time there will be one of these types of people, and we've all been guilty at some point too.
Slow people -
Some people are slow when getting on the plane, but getting off is the worst. Sometimes people will take their sweet time and walk into the aisle and get their bags from the overhead compartment while there is nobody in front of them. Everyone, not just me, wants to shove these people out of the way.
Your sibling -
By far the worst person to sit next to. It's like sitting next to concentrated evil. It's best to write these sort of things to keep your mind off them, and to keep them curious.