The above chart shows the top users of electricity in a typical US home. The data are from the EIA and date from 2001 so it might have changed a bit but probably not all that much. Note that this is only electricity usage, not all energy usage.
So if you want to conserve, you can see where are the likely highest priority places to start. Of course, these are national averages so you can make regional or personal adjustments. For example, if you live in the southern parts of the US, air conditioning is likely a bigger fraction of your total, while in northern climes, it's probably less. Similarly, if you heat with electricity then space heating is likely the biggest bar for you, whereas if you don't, it will be zero.
Still and all, if you start working down the bars in size order and replace anything that is old and inefficient with new and maximally efficient replacements, this will be a fairly rational approach. This is likely to save money in the long-haul, and at least in some states (like New York) you can get long-term financing which will mean that you can replace a bunch of your appliances with no cash up front - it's essentially new appliances for free (since the utility bill savings should exceed the loan payments). What's not to like?