
----Hot Blood and Pure Heart----
Not only does he remain one of the series only true innocents, Gai also manages to suffuse his every action with real passion. Although there are a number of characters who have similar levels of emotion, they are often painful, selfish, or hateful feelings; a desire to be seen (Naruto), a desire to be appreciated (Lee), a desire to get back at those who've wronged you (Sasuke and Neji), an unexplainable anger at anyone and anything for reasons you don't even fully understand yourself (Gaara). In contrast, Gai's passion is as pure as his intentions.
This is why he serves as the perfect break in tension for the series as a whole. When the audience needs for the drama to be dispelled (if only for a few moments), they throw in Gai caterwauling and making a scene over Lee accidentally taking a bottle of sake. Or, if there has been more than enough intense emotion for the past handful of volumes, they have Gai offer Kakashi a piggyback ride back to Konoha. And so, the painful or tenuous scene is dispelled.
The reason that these jokes work, that one is able to allow Gai to intrude in such a manner is in part due to that innocence, that passion which works through each of the man's flamboyant actions. And, it's that same passion, innocence, and tension-breaking ability that earns him more than the usual dose of affection from me.

----Laugh and the World Laughs With You----
As was mentioned in the talk concerning passion and innocence, Gai-sensei knows precisely how to steal a scene, even if he is never doing it purposely. The key to the majority of these scenes is their humor. No matter how many times I watch the opening of the Chuunin arc and see the first Gai/Lee sunset, I laugh.
Hard.

It's amusing in an idiotic, wonderful way. When Gai gets upset at being ignored by Kakashi, when he swivels his hips in a way that no human should be able, when he yells at Lee to "Take them off!", all of these and more appeal to the childish side of me. And, if I forget all of the other contributions that Gai has made to the series, I will never forget all of the great laughs he's given.
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Spoiler: Links to Good Gai Fanfiction