Goggles
I've tried-and-tested so many goggles, that I have a cupboard full of them. I've tried swimming pool race goggles, through to wide view, almost diver-style ones. I finally settled on Barracuda Triton goggles - I think these are awesome. A combination of good vision, but not too big on the face - the problem I had with the bigger goggles, is that I just couldn't get a good seal.
Tips
Take two pairs of goggles into transition - you never know when one will break, or another triathlete needs to borrow a pair. I take one smoke and one clear lens pair with me, so if it's early-morning gloom or overcast I choose the clear; sunny and bright the smoke lens. I have one Barracuda goggle's case, and I can fit both pairs in there.

Always test your goggles before using in a race, especially in open water. I trialled a pair in the pool and they worked great - they offered the best visibility of any goggle I tried, so thought they'd be great for swim-sighting. However, once I hit the more turbulent nature of a triathlon start, and the rougher conditions of open-water, they leaked terribly - and trust me, this sucks big time!
Bike
The most expensive piece of triathlon gear.

I ride a 2008 Felt B2 Comp which is frame-only (carbon), with the components coming from my broken 2008 Felt B12 (the frame was swapped for free by Bike Haus). The only alteration I've made to it, is the saddle which is an Adamo Racing Saddle made by ISM. Additionally I have an X-Lab bottle rack behind the seat and a SpeedFill hydration system on the frame, which has a straw extending to the handlebars so you can re-hydrate whilst in the aero position.

I use a Garmin Edge 305 (GPS) bike computer, with a cadence sensor mounted - this is a great gadget. You can customise the screen to have up to 8 fields of data. I set it up to have Average Speed (so I can estimate my bike-leg time on-the-go) on the top line, then Current Speed (am I currently below or above the average) on the next line. The third row is split to show Distance and Time, with the final row having Cadence and Average Cadence. The computer allows a second screen to be shown, and on this I have similar data but showing lap data.
Tips
It's not all about a tri bike
There's no need to be paranoid about having a proper tri bike. Many of my friends ride road bikes and are damned good on them. I did my first race on a nobbly-tyre mountain bike, and you'll see all sorts of gear in a race.

Get clip-ins and practice
Cycling in clip-in pedals is much more efficient, but it's worth practicing in them, as they can take getting used to. On one training ride, someone turned up with a top-of-the-range bike and all the gear - at three traffic lights in a row, he fell off sideways as he wasn't used to unclipping - I laughed hard! My mate Kyle has cycled without them for years, and still puts in awesome bike times, but he has finally realised that he can go quicker with them - the 2011 Ironman 70.3 will be his first race in them - hope I don't end up laughing at him!

Bike set-up
Get a good bike shop to set up your position on the bike - I was amazed at how wrong my position was, and how much better it was after getting it changed.
Running Shoes
I'm racing in Zoot runners at the moment, these are designed for triathletes, but I don't notice any particular difference between these and ordinary runners. They come with elastic laces, and a high back for pulling on easier in transition, although if I run without socks I blister under my arches after a few Kms. This makes me think they won't be good for fast transitions, but in a half-ironman I'm willing to sacrifice time for a bit more comfort - and in an Olympic I can probably put-up with the blisters. Since reading Born To Run (by Christopher McDougall; great book, highly recommend it) I have preferred a thinner sole, the Zoots aren't "barefoot", but they're less padded than normal shoes and are quite light.
Tips
Get elastic laces in your runners.
Saves so much time getting the things on your feet!