One of my favourite parts of a bicycle frame's anatomy is what's called the "seat cluster" - the joint where the seat tube, the top tube, and the rear stays of the bicycle meet. If done nicely, the seat cluster can look like a beautiful starburst of lugwork, and that is what I love about it. On the picture above is the very classic seat cluster on the Waja trackbike I rode in Vienna earlier this summer.
A similarly classic seat cluster on the Rivendell Sam Hillborne.
[image via Franklyn W]
And another example from an Ebisu bicycle. You can see how the individuality of the cut of the lugwork interacts with the colour of the paint to create subtle variations in form and shade. The stay caps (those narrow diagonal pieces that taper to meet the main lug) can be rounded or pointy, flat or concave, stubby or elongated.
[image via cycleczar]
They can even wrap all the way around the main seat lug, like on this Toei bicycle, so that the pointy tips meet. This is called a "wrap around seat cluster" design.
The stay caps also make for a good surface to embellish with an engraving of the manufacturer's name, like on this vintage Trek 610.
[image via Dancing Weapon]
Or with hand-painted flourishes, like on this Bob Jackson.
[image via Royal H.]
They can also be carved, if so desired, like on this early Royal H. frame.
[image via ribalrid]
While I prefer classic seat clusters, there are also many designs that deviate into all sorts of creative directions. On this Bates B.A.R. bicycle, the seat stay caps look like sharpened pencils and meet the main lug at the bottom.
[image via somervillain]
On this vintage Trek 560, the seat cluster is one big lug, and the seat stays are held by lugged sockets at the back.
[image via Kevin Saunders]
And then there are seat clusters where the stays connect to the tube directly, below the lug, like on this Formigli frame. (My understanding is that both this and the method used by Trek above is done to create tighter clearances?)
[image via Royal H.]
A similar approach to "fastback stays" by Royal H., with the seat stays attached at the rear.