This surprising revelation was made in the audio commentary included with the episode "Plankton!" On the DVD boxset of the show's first season. The disc does not establish which characters match up with each sin, but as an avid Spongebob fan, I believe the comparisons are fairly straightforward:
1. Greed (Mr. Krabs) - this is by far the most obvious comparison that can be made. The avarice of Eugene Krabs is made painfully clear throughout the series. He is constantly thinking of ways to turn a profit, even if it involves taking advantage of his friends or putting them in harmful situations! In one episode, he sings a song called "If I Could Talk to Money"...and there's even a wiki page devoted to compiling all of his greedy plans!
2. Envy (Plankton) - another no brainer. With all of Krabs' wealth and good fortune, there has been an equal amount of hard luck and failure for his archrival, Sheldon Plankton. Plankton owns a struggling restaurant called "The Chum Bucket" and is consumed with the desire to achieve the success of his adversary. His life's goal is to steal the Krabby Patty formula from his Krabs and drive his primary competitor out of business.
3. Sloth (Patrick) - the guy lives under a rock for crying out loud! If that isn't enough to convince you, in the episode "Big Pink Loser" Patrick is given an award for 'doing absolutely nothing longer than anyone else'. He then proceeds go back under his rock to protect his title.
4. Pride (Sandy) - the fact that Sandy Cheeks is from Texas alone should almost suffice for this one. She is a squirrel that is very proud of her heritage, so much so that in one episode she nearly moved back home! Sandy also takes a great deal of satisfaction in being the only land critter living down in Bikini Bottom among all the fishy folk. Though generally a good-natured individual, Sandy is quick to spout off about the greatness of the Lone Star state or to show off her athleticism in a karate match or a weightlifting contest.
5. Wrath (Squidward) - Squidward Tentacles has no qualms about expressing his negative outlook on life, whether it be by describing how much he hates his job at the Krusty Krab or through outward disdain for his two obnoxious neighbors. He is portrayed as a general failure who refuses to acknowledge his own personal flaws. This constant self-denial manifests itself in a sarcastic sense of humor and resentment toward the society that doesn't 'appreciate' his creativity and clarinet...erm..."skills".
6. Gluttony (Gary) - now this one's a bit trickier. Those who have watched a great deal of the series will have noticed a number of jokes about Spongebob having to remember to feed his pet snail. To be honest, Gary doesn't do a whole lot besides eating and meowing, and the meowing is often due to the fact that he is hungry. Once when Spongebob hadn't fed his pet, Gary is shown eating parts of their couch! In another episode, Gary runs away from home because Spongebob forgot to feed him for a while. Another time when Spongebob had amnesia, Gary ate a year's supply of snail food and became morbidly obese! This proves beyond a doubt that when left to his own devices, Gary would rather do nothing but eat.
7. Lust (Spongebob) - our final analogy is probably the least apparent because we typically think of 'lust' in a sexual sense. However, the alternative definition for lust is simply "a passionate desire for something". In this sense of the word, it cannot be denied that our absorbent yellow friend is an extremely lustful creature. Spongebob has a lust for life that is incomparable to most other cartoon characters - he yearns for the affections of both friend and foe alike, is eager to please, and will often stop at nothing to complete a task.