Everyone has given excellent suggestions.
I don't know if anyone mentioned utility costs. If you're in a hot or cold part of the country, that's important to know whether the place has decent insulation, etc.
And "wonder" if there is too much pot pourri or something in the house, it could be covering up mold or animal smells.
Don't make an offer if they won't agree to inspection.
Be sure to find out how old the appliances are, too. New refrigerators, etc. are expensive to replace.
Check on storage space - is there any? (That's an issue in Hawaii - they build w/o anywhere to keep anything.)
And the neighbors - several people have mentioned it. You want to see the neighborhood at night, and on the weekends. Some very nice, quiet neighborhoods are madhouses when the residents are home.
We all know that there is rarely a "perfect" house. When you look, keep in mind what you'd eventually want to change. (Cabinets, counter tops, appliances, carpeting, etc.) If that list gets too big, the house may not be for you.
Good luck!!!