As noted by Jay, the first photo you linked is using a very extreme level of magnification, and it appears as though it was "focus stacked" to achieve total clarity.
It is possible to get close-up eye shots like that (although not quite as magnified as the first shot) without that much extreme magnification. A 100/105mm macro lens can get you pretty close, however you will need a LOT of light illuminating the iris to allow you to keep your ISO lower, and still take a shot where noise doesn't interfere with fine detail. A macro lens with extension tubes will also get you in pretty close. Don't be afraid to use a moderately high ISO, so if you can't get enough light to get the shot at ISO 100 or 200, try 400 or 800. You need a willing subject as well, as you'll probably still be working with a fairly low shutter rate despite everything.
The closer you focus and the more you magnify, the thinner your DOF will get. Sometimes, even with a very narrow aperture, you just can't get enough DOF with a single shot. Use continuous shooting, and if you can, a cable release and tripod, and get several sets of sequences of shots. Adjust focus just a tad between each set of shot, pick the best one or two shots from each set, and use a program like CombineZP to stack the focus from those shots into a single photo.