Jack and Algernon certainly are a lot alike. So much so that it feels like we’re writing a Siamese twin character analysis. Take a look at the first section of Jack’s "Character Analysis" and come back for more Algernon-specific details.
Algernon is a toned-down version of a character type Wilde enjoyed writing: the dandy. A dandy is an educated, dedicated follower of fashion... and a flouter of conventional male duty. Today we might call them metrosexuals. Appearances are very important to Algernon, especially neckties and buttonhole flowers. He doesn’t hide his vanity from Cecily, confiding that "I never have any appetite unless I have a buttonhole first" (II.71), and that Jack "has no taste in neckties at all" (II.57).
In An Ideal Husband, the play Wilde wrote just before this one, a similar character (with a similar girlfriend) appears. This character, Lord Goring, even has a scene with his butler that resembles Algernon's first scene with his butler, Lane. Wilde wrote that Lord Goring "plays with life," and the same can be said of Algernon.
He's full of mischief. He loves champagne and he’s bad with money. His glee in finding out Jack’s country address is irrepressible. He falls in love with a girl and proposes to her within ten minutes. And even when things get messy, Algernon can’t stop excitedly eating muffins. Algy treats life like a game, which makes reading The Importance of Being Earnest all the more fun for us.
Algernon’s not one to lecture about the status quo, but he seems aware of the absurdities of Victorian high society. He responds by taking absolutely nothing seriously.
Jack: Oh that’s nonsense Algy, you never talk anything but nonsense.
Algernon: Nobody ever does. (I.299-300)
Like many of the characters in the play, Algernon embraces fiction in his daily life. He creates "the invalid," Bunbury, with flair, and clearly enjoys reporting on the imaginary invalid’s health to Lady Bracknell (who we suspect knows he’s full of it). Algernon argues passionately for the existence of Bunbury:
Nothing will induce me to part with Bunbury, and if you ever get married, which seems to me extremely problematic, you will be very glad to know Bunbury. A man who marries without knowing Bunbury has a very tedious time of it. (I.94)
For Algernon, creating fictions is a necessity in this society. But it doesn’t have to be unpleasant. It’s this perspective that makes him such a good match for Cecily... who is equally whimsical. Think about it: you meet this girl for the first time, and five minutes later she’s reading from her diary about your whole romantic history together. This might seem just a bit strange.
But in the world of this play, and particularly for Algernon, this fantastical approach to life is just what he needs. He "buys in" to her fiction, getting upset when she comes to the part about breaking up. When we finish The Importance of Being Earnest, we get the sense that Algernon could not have written a better ending himself.