As soon as you have gone through a kit beer or two so you understand the process, it is great fun to make it a little more difficult (and rewarding) by adding some grains and maybe some hops.
Bascically beer is made by extracting malt sugar from grains, boiling this sugarwater (wort) with hops to create bittering/flavor and then cool before fermenting with yeast.
If you have done the kits already, you can improve the beer by trying any of the following
-another yeast, different yeasts will give different flavored beer (English, US, belgian, etc)
-add some grains (darker grains for colour and flavour, carapils for better body/foam, etc)
-add more hops (for freshness, more bittering, or just to give it your very own flavour)
All three are easy to play with and a quick search here or on google will get your fingers itching to try something new!
The probably biggest improvement you will make to your beers is when you are able to control the temperature.
Many of us use a fridgemate/tempmate which basically cuts the power to a fridge when the fridge reaches the temperature we want. this makes sure the beer ferments at a temp of our choosing, creating cleaner tasting beer with less "twang".
They look something like this
http://www.beerbelly.com.au/measuring.html or your local homebrew shop.
Next time you are brewing, try steeping some specialty grains to make the beer "unique". It will be a recipe you made up, no one else will have the exact same thing (for better or worse!)
It is as easy as heating some water, dump the grains in and after say 15 mins you get the grains out,. Having the grains in a netting bag makes it easy, some use a coffee plunger. The resulting "grain tea" is added to your fermenter as part of the sugar you would normally add from a box of brewing sugar.
thanks
Bjorn