Good luck! Looking for and buying a house can be one of the most stressful things a person will go through, but in the end it's worth it.
Some things we looked at:
1) Furnance and Oil Tank. These aren't cheap to replace, so as when the last time they've been serviced was. If you see any leaks, tell the seller that they have to get it fixed before you'll even consider.
2) Roof. Roofs generally last about 20 years or so, so if you can notice any buckling, lifting, or anything that looks like it's in rough shape, again negotiate that to be fixed. Find out how old it is. When you go for insurance, they'll want to know before they'll insure you. Even if it's an approximate age it's fine.
3) Electrical. Not sure about wattage/voltage, but it's best to find a house that has upgraded electrical to circuit breakers especially if it's an older house.
4) Mold. Especially up in the attic, check to see any signs of mold. If there are, you may want to reconsider.
5) Structural/wood damage. Anything that might be a sign of termites.
6) Water damage or signs of water entry, especially in the basement. There should be a sump pump if there is any history of water entry, and if there isn't a sump pump, I'd personally stay away. I felt wary even looking at houses that had them just knowing that water did come in. Every basement has some water issues, even if it's condensation from pipes (which we have), but look for any visible signs or an overly musty smell.
7) What method of heating is used, oil, gas or electric. It's good to ask around and research how much it would cost to heat/use the stove using each method because some are more than the other. You'd hate to move in and find out that you could've saved $200 a month if the house had only had one method over another.
8) This is sometimes overlooked, but check to see how clean the house is. This is a good indication of how well the house was taken care of. We looked at houses that still had dirty dishes in the dishwasher, food in cabinets, and just all unkept appearance.
9) Water Pressure. You don't want to find out that you have no water pressure and it'll take you an hour to take a shower
10) Lead Paint - Some older houses still have lead paint, and you can pay for an inspection to find out if they do have it. It doesn't have to be removed, but if you have kids, even if you have hungry kitties, you could have problems. I believe some insurance policies may not look well at a house that still has lead paint.
11) Town Sewer or Septic - It's important to know because you'll have to either pay for the sewer on your water bill, or you'll have to pump out your septic tank every few years. If it's septic, ask when the last time it was pumped. There is another thing my dad said to ask about with this but I can't remember what it is.
12) Remember to have an inspection by a private inspector, not one the seller sets up and not one recommended by the bank, one you pick out. He'll point out all these things anyway.
Other than that, look at things that might have to be replaced or redone like carpeting, other flooring, wallpapering, painting etc.. because you'll have to factor all those things in cost wise. I wouldn't get hung up on things like doors that might be sticky or not close all the way. All those things can be fixed rather easily, and things change with the weather anyway. Windows, unless they are severely drafty, can be changed eventually and they can be written off on your taxes. It's still not a bad idea to ask how old they are, just to know.
Remember that every house has it's little imperfections unless it's brand new, and to not get hung up on the little things. They can be changed over time.
Make sure that you get a house that is large enough for what you need right now, or as long as you think you may be in the house. You might have to compromise if price is an issue, but it's something you really have to think about. We put an offer down on a house that we wound up losing that now that we think about it, if we had gotten it, would've been too small and we would've been miserable.
That's all I can think of right now, all the things I learned from when we bought our house and I knew to ask when I looked.