I’ve always tried to remove the smoke detector batteries upon moving into a new place. Those things go off every time you cook anything.
Take a good look at and inside the kitchen and bathroom cabinets–it’ll give you a good idea of how the rest of the place is put together.
For me the first rule is: don’t buy anything new whatsoever, until you have lived there for a while and determined that you cannot live there without it.
It is so easy to clutter up an apartment with stuff that you could easily store if you were in a house. Don’t buy all those separate kitchen gadgets that you only use once a month or less, cleaning goop for every possible different surface, or any furniture you don’t actually need. An apartment can be as roomy as a house if you don’t fill it up with stuff.
Secondly, do a thorough purge of your belongings before you move in. I gave away or sold more than half my clothes and about 10% of my books and CDs; I wish I’d got rid of more.
When I used to arrive home after work I spent maybe half my free time cleaning, renovating, or fixing stuff; now in my apartment (well townhouse really, same diff) I take my coat off and the evening is my own. Every item you buy is one more thing to look after, you will free up so much of your life by just not owning stuff you don’t actually need.
You’re no fun.
They might go off anytime YOU cook anything, but normally, they won’t. Unless you’re doing some kind of barbeque, regular cooking rarely has enough smoke to set off an alarm. If this is the case, then you are either burning your food (whuich, if you like it that way, whatver) or might just need to give your oven and stovetop a good scrub.
That being said, I still wouln’t have a smoke detector actually in the kitchen itself, since at some point we all make mistakes and will burn the roast. 
But you should always have at least one (preferably two) smoke detectors currently working in an apartment. Taking the batteries out of them is not a good idea. If your neightbors place catches on fire in the middle of the night and the wall you share with him starts to smolder, a smoke detector waking you up could save your life.
I don’t burn my food, and my kitchen smoke detector goes off whenever we use the broiler.
Buy a fire extinquisher. Everything else comes with practice.
Not necessarily. I had one that would go off when the kettle boiled. Literally.
If you have stuff: professional movers don’t cost as much as you might think! For a small apartment, and if you pack very well in advance, you can get moved in town for around $250. It’s worth it. It means that you can actually enjoy unpacking and setting up on moving day, instead of spending it killing yourself and your friends, and then spending that night laying among the boxes, groaning.
When you talk to the neighbors about maintenance etc., also ask about insects and mice. An occasional roach is inevitable, but if you keep the place clean AND the landlord is on the case, you shouldn’t see them every day. Decide for yourself if you can endure mice or not (your prospective cat may or may not remove them for you). If the neighbors mention rats, go somewhere else.
Don’t forget renters’ insurance! Get replacement-value coverage; it costs more but is worth it.
Some have mentioned students as bad neighbors, but I would add a qualifier: Undergraduate students are bad neighbors. Graduate and professional students, with few exceptions, are too tired and busy (and broke) to be rowdy.
I heartily second the recommendation to turn on the hot and cold water when viewing the apartment. Also, visiting the place in the winter, if possible, is the best way to learn how adequate the heat is.
Searing meats on a stovetop will fill the kitchen with smoke without proper ventilation – best to avoid high-heat cooking if you have no windows or the inadequate hood which, if included in the apartment, will be insufficient 100% of the time. Might as well chain smoke a couple of packs of cigs, for all the good it will do you to stand around in a hot, smoky kitchen.
I’ve used “professional” movers the last two times I’ve moved – they’ve been great, and I have a lot of heavy stuff. Price goes up as the amount of stairs increases. $300 max, in my case, but these were unbonded guys, so it’ a worry if one of them were to fall and injure himself.
Loud neighbors suck – the one’s I’ve been privy to have in fact been undergraduates. I had two of them sharing the apartment evicted, by telling the landlord all about the really terrible stuff, and had the police actually show up maybe four times to investigate, in the hopes of scaring them straight. But keep in mind, you do have the right to enjoy your own music, without headphones, in your apartment, just as others have the right to peace and quiet in their own apartment – these are relative terms, and you’ll have to discover the correct balance between being obnoxious and being a good neighbor, and it’s different everywhere you’ll live. There are real bastards who will get extremely upset at “cooking odors,” however mild, running a shower at 3:00 AM, the footfalls caused by bare feet – you shouldn’t allow yourself to be cowed into lying in a prone state afraid of moving about, just as you should always be aware of the more disruptive activities you may not be conscious of performing (stomping around in heels/boots, loud TV, etc.). It takes some getting used to, to judge what’s appropriate and what’s not in an apartment.
Live on the highest floor, if possible. I am one of those people who is bothered by constant walking and squeaking above me, and I was irritated by it a lot in the first apartment I lived in. Not enough to complain or anything, but enough to move to a unit on the top floor (well, I didn’t just move for that, I moved in with someone). If you have to live below someone, make sure it’s a spinster.
My last two “apartments” have actually been houses that were sectioned off into four and two units, respectively. It is much more calm than living in a complex with a lot of other people, and not any more expensive, at least around here. Fewer neighbors, and the sound is usually better insulated. Look into it.
Even if your apartment is advertised as “pet friendly,” get it in writing from the landlord and make sure he/she knows you have a cat. I ran into problems with this at my last apartment–someone at the office (who was not the landlord) said it was pet friendly, I got a cat, a few months later the landlord came over for a surprise visit and was super pissed and I had to pay a pet fee and cleaning fee. Live and learn. Some places (like mine) make you pay a pet deposit; mine was a full month’s rent, which I will get back if the apartment is not dirty.
Oh and that reminds me: keep it clean. You don’t have to obsess over it, but you also can’t let the place turn into a sty (I’m talking rotting food, catshit on floor, etc). This is not your property and they will charge you for it if you make it unlivable for the next person. Not that I’m saying you would, of course, it’s just something to remember.
Thanks to all who replied. This will be my first apartment alone, but I have lived in a few apartments with my parents. I have thus far had little success looking in the city that I attended college in. Due to the past hurricane season, many complexes were damaged, others are quite full, and apartments that come up for rent stay available for only a few hours after the day’s paper (with their ads in) comes out. Apartments rented by private individuals go quickly–I’ve missed some by mere hours. It’s somewhat discouraging. I have been looking for a few months now–this isn’t just something I decided to do on a whim.
I am thinking of moving to a different city in this state, or a different state altogether. As much as I like this town, there doesn’t seem to be room for me in it.
I will take all your advice into consideration, however, and thanks again.
Another point to add on the “keep it clean” comments. Not only does it help ensure that you’ll get your deposit back when the time comes, but the place will seem bigger when it’s tidy. In a one-bedroom, it will make a huge difference.