This depends a bit on the kind of wine you're making. I can only speak from my own experience making Pinot Noir and Chardonnay:
You will need a grape press. Some homebrew shops sell these, and some also rent them. With Pinot, you will de-stem the grapes and ferment the whole berries, punching them down gently with a punch down tool several times per day to mash things up a bit. But when the fermentation is done, you'll need to press the rest of the juice off the skins and seeds into...
A barrel. I've made home wine with oak chips in a carboy, but if you want to do things right you'll need to invest in a barrel. The Beverage People in Santa Rosa sell 5, 10, 13 and 30 gallon reconditioned French Oak barrels. I think I paid $275 for a 15gal last year and it's working nicely to age a bit of leftover commercial chardonnay.
If you're making cab, merlot, petit sirah, syrah, zin, etc you'll want to crush the fruit before you press it. You can buy mini crusher/destemmers to simplify this process. Or you can just stomp the grapes in a bin. Having a big fat Italian woman to do this helps a lot.
If Chardonnay, you'll press the fruit before you ferment it, eliminating the need for the punch down tool.
A good pH meter is a must-have. You need one that reads down the the 100ths because there's a big difference between a pinot with a 3.6 pH and a 3.69 pH. It's important to keep your pH in the safe range when fermenting because...
...You're not going to be fermenting in a carboy with an airlock. We open ferment our wines in a big plastic bin. If your must is fermenting at too high a pH, spoilage bacteria can thrive in it.
Breather bungs for your barrel. When you press your wine to a barrel, it's still going to need to go through a secondary fermentation, called malolactic fermentation. Gas needs to be able to escape. I suppose you could use an airlock for this, but we use breather bungs at the winery. You'll also need a solid bung for aging your wine.
Gallon jugs. You'll need some gallon jugs with airlocks for leftover "topping" wine. You'll need to periodically top off your barrel to make sure your wine doesn't oxidize, and you'll need some containers for this.
As mentioned before, you'll need a corker.
Some winemakers like to stir the lees back into the wine from time-to-time. If this is you, you will want a lees stirring tool.
Oh, most important of all: a wine thief. You need to be able to taste your wine as it ages!
A mini bottling line would help a lot-- something with a catch basin in it and a shut off to prevent overflows. This way you can hoist your barrel up and gravity feed the basin while you're bottling. Speaking of gravity-fed bottling lines, here's a photo of ours this spring... yikes!
That's about all I can think of right now.