How long has the house been on the market? How many viewings have there been?
Is the vendor open to offers? (you have to read between the lines when an estate agent gives you his answer to this question, but sometimes they say "well, there's been a lot of interest in this house so I think they are hoping to get near the asking price" and other times they say "well, they are keen to make a sale so put an offer in and see" (meaning yes, offer quite a bit under the asking price).
Will help you decide what offer to put in if you like the house (eg if it's been on the market a while they would be more likely to accept a lower offer than if it's only just gone on the market).
You will probably have questions specific to your situation - eg how long does it take to walk to the station / town centre / local supermarket / park.
Oh, really important (if the house isn't chain free): what is their position regarding moving out? If they haven't already found somewhere to move to, then once you put the offer in, you might have quite a wait before you move in, and if they can't find somewhere to move to, then they might withdraw from the sale altogether. We have recently bought a house and the vendor of the first house we put an offer in on said he'd be moving into rented, but when he received our offer he started trying to find somewhere to buy. We couldn't hang around waiting for him to buy somewhere, so we withdrew our offer.
Good luck - it's an exciting time!