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Cowboy Bebop Guns

Spike

Faye

Jet

Others

Other Guns
Looks like a .38 caliber to me

As mentioned earlier, firearms in the late 21st century aren't that much different compared to today. Except for a few exceptions, the small arms seen in Cowboy Bebop are pretty much standard fare.
However they differ from other anime series guns in their variety. Here, the mechanical designer really show that he had done his homework.
Ranging from pistols, machine-pistols, sub-machine guns, assaults rifles and shotguns including a derringer (session 6 Sympathy for the Devil), a revolver (above, seen in session 16 Black Dog Serenade), a sniper rifle (same session) and even a multiple grenade launcher (session 14 Bohemian Rhapsody), the attention to detail  in the weapons is simply amazing.
Take note however that I am not attempting to include every single weapon depicted on Cowboy Bebop. What you see here are merely what I consider to be notable enough to merit description. In this way I hope to showcase the remarkable versatility of the Cowboy Bebop creators and the universe they have created.
Due to the large number of guns in this section I have decided to divide them into 4 sub-sections for easy perusal.

Sub-machine guns

Machine-pistols

Assault Rifles

Shotguns