There are several reasons to upgrade to a dedicated server, but the most important one is that you get your own dedicated IP address -- no one else can use or abuse that IP, and if you keep it clean it will always be clean.  By clean I mean not listed in any spam databases or on any search engine blacklists.  When you are first assigned your IP make sure that you verify the address is indeed clean by checking the most common blacklisting databases.

With a squeaky clean IP, you will have the best chance at good search engine rankings, and will get better email delivery to your customers.  I've seen sites go nowhere in the search engines, but when moved over to a dedicated IP they take off like a rocket -- if you live in a bad neighborhood, you get a bad reputation!

There are many other benefits to a dedicated box as well:

• Root access to customize the box to your specifications
• Site pages load faster because you have your own dedicated RAM
• The processor is all yours, not shared with thousands of losers
• Better customer service -- you're considered a higher class of customer
• You can do what you want -- lots of shared hosting sites are telling people that they cannot run certain scripts or applications due to server overload

If your budget will not allow you to get a dedicated box, make sure you at least get a VPS (Virtual Private Server), which is a dedicated box that is "chopped up" into specific areas, each with its own RAM, CPU, root access, etc.  VPS is cheaper than dedicated, but is still light years ahead of the standard shared hosting.  Some shared hosting is better than others, but you will still be better off with a dedicated box or VPS.