I started with a Mr. Beer kit so my first upgrade was a 5 gallon starters kit that had 2 buckets, racking cane, hydrometer, carboy brush, paddle, airlock, etc... All the basics. Quickly I found I needed larger kettles, so I scoured garage sales for the largest stock pots I could find. This served me well while I was doing partial boil extract kits.
The first upgrade that wasn't absolutely necessary, and one of my favorites so far is my Vinator. It makes bottling day so much more enjoyable. Just fill it with sanitizer, a few pumps into the bottle and your good to go.
Speaking of bottling, when I bottle I like to design a custom label. I go to fedex and use their color laser printer, cut them out and fix them onto the bottle with milk. A sort of 'upgrade' is to use BottleMark.com to design custom caps that match the labels.
My latest two upgrades are less than a week old! I went out and bought a keg system so that I could force carb a beer that I'm trying to rush for a christmas party. This beer I brewed had a 3.5 gallon boil which my kitchen stove had a hard time getting to a roiling boil, so I went out in search of a turkey fryer on sale. No luck finding one on sale, but I picked one up anyways at full price. I now have a 32,000 BTU propane burner with an aluminum 7.5 gal pot. (I could have gotten a 45,000 BTU burner for $15 cheaper, but the stand looked a little flimsier. I figured 32,000 is still about 3x the heat output of my kitchen stove.) Im still doing 5 gallon batches so I'm hoping it will work.
Upgrades I am looking at getting in the near future are a wort chiller, refractometer, and the hardware to make a kegerator or keezer now that I have the keg and co2.