This may be one of the more obvious factors, but you want to be sure you're satisfied with the location of your new home. What's important to you? Area schools, communte, walkability, safety? Make a list of your location deal breakers and stick to it. A great home might dazzle you, but as the years pass and the new home excitement wears off, you won't want to be stuck in a location you don't love.
The area might be a great fit, but what about the neighborhood? When you're seriously considering a home, visit on week days and weekends, evenings and daytime. Pay attention to resident behavior and the neigborhood atmosphere and see if it's in line with your expectations.
Beyond neighborhood and location, are you happy with the way the home is situated? Is the yard private enough for you? Are there too many stairs? Is the yard safe for children or pets? Again, a home could be a great fit on the inside, but little situational problems can become glaring problems over time.
Of course, you want to be comfortable in your new home. You may also want some room to grow a family or host out of town guests. Think about how your new space will be used and whether or not the size fits your current lifestyle and your future expectations.
If you tend to cook regularly, entertain guests, or generally use the kitchen as a gathering space, paying special attention to the kitchen as you house hunt is crucial. Appliances can be replaced, walls can be repainted, but changes in layout can be costly and time consuming. Make sure you're happy with your counter space, eating area, and walking space.
Older homes tend to have smaller storage areas while newer homes usually take extra storage into consideration. If you have a lot of extras - sporting equipment, garden supplies, holiday decorations, etc - be sure to take this into account as you look.