The Krawk
To get a Krawk as a pet, you must first have a Krawk Petpet equipped to any of your pets, and less than 4 pets in your account. Go to the Fungus Cave and your Krawk petpet will be magically transformed into a real-life Krawk Neopet! Another way to get a Krawk is to use a Krawk Transmogrification Potion on any of your pets, and also note that this method is a lot cheaper than buying a Krawk petpet. Also, Krawk Petpets are not bought at the Little Nippers shop at Krawk Island, but instead at the petpet store at Tyrannia. Odd, no? This article should explain it :)

The Draik
By buying a Draik Egg and bringing it to the Draik Nest in Meridell, the egg will hatch and a Draik of whatever color the egg was. Surprisingly, Draik Morphing Potions can cost MORE than eggs, so you might want to try that.

The Grundo
The ever-so-lovable Grundos can be adopted at the Space Adoption Agency without fees, and come in seven cool colors.

The Cybunny, Kiko, Chomby, Tonu, Jetsam, Koi, Poogle, Hissi and Lutari
These pets have no specific way to be gotten, but you can use morphing potions or transmogrification potions on your pet to turn them that species. Also, on their species day (e.g. Cybunny Day), Neopets might just release a couple of their kind :) Remember that Lutaris will disappear if you abandon them, so they are the only species that can't be transferred.