Which Comes First, the Purchase or the Sale?
This is the classic "chicken or the egg" question as it applies home buying and selling. It is also the toughest question in real estate, and one that most every homeowner will have to answer at one point or another in their lives. The basic dilemma is this: You decide you would like to move, and you are an existing homeowner. Do you put your home up for sale immediately and face the possibility of selling your home quickly and having nowhere to go? Or, do you hold off on selling your home until you find one you want to buy, and then face the uncertainty of not knowing when your original home will sell (and, worst case, maybe having to make two house payments)?

Clearly, there is no right or wrong answer here; it is purely personal preference.
Assuming that you will have to make this decision at some point, here are the two schools of thought and the advantages and disadvantages of each:
Buy Next Home Before Selling Current Home
Advantages:- You have eliminated the risk of not knowing where you will be moving next
- You can take your time in making the decision of buying your next home, increasing the chances that you will make an intelligent, rational choice
- Your offer on your future home will likely include a "home sale contingency," which will make your offer less enticing to the seller (in fact, many sellers - and most relocation companies, which are typically involved in sales relating to corporate transfers - will simply not entertain offers that include home sale contingencies)
- You do not know exactly what your current home is really worth (because you haven't sold it yet)
- You may have a hard time selling your home and you may end up making two payments (one on your existing home, and one on your future home)
- If you get a bridge loan to finance your purchase (which is typically the case is such circumstances), you may end up with three payments (one on your existing home, one on your future home and one on your bridge loan)
Sell Your Current Home Before Buying Next Home
Advantages:- From a financial perspective, you can proceed with confidence (as you have the advantage of knowing exactly how much your current home is/was worth)
- You will not need to include a "home sale contingency" with your offer on your next home, making it much more attractive to the seller
- You may have to find your next home rather quickly
- You take the risk of possibly having to buy a home that is not perfect for you (or of making two moves; one into an apartment as you continue to look for the right home, and then into your new home after you have finally found it)
Again, this is clearly a personal preference issue. We have always believed it better to sell your home before buying your next home. We think the advantages outweigh the potential disadvantages of using this approach (particularly with regard to the whole "home sale contingency" issue). In our personal dealings in real estate, we have never included a home sale contingency in an offer because we know how unappealing these contingencies are to sellers.
Having said that, again, there is no right or wrong answer here. It's whatever you are most comfortable with.