Often when I have a really hard problem to solve I resort to Scheme for the powerful set of patterns that it supports. Here is a smattering of the results and tools that I have accumulated.

Pure Scheme

Universal equal? for Scheme
The moral equivalent of the exit routine of Ansi C and Unix.
Transposing a ragged matrix
Persistent Stack Frames
Tax
Code to enumerate free variables in a Scheme expression

(      (lambda (arg) (list arg (list (quote quote) arg)))
(quote (lambda (arg) (list arg (list (quote quote) arg)))))

Applied Scheme

Some number theory.
RSA (4 times standard speed), Extended Euclidean Algorithm
A matrix inversion routine not tied to floating point scalars.
Set abstraction for totally ordered types
Merging and Sorting
Multivariate polynomials, Multinomials and Differential Geometry
Random Normal Deviate generator; requires rand31 from here.
Generalizing Complex Numbers. Dynamic creation of new types.
Clifford Arithmetic
Sneaking up on Multiple user Scheme, meta stuff
RC4 stream cipher

Scheme Theory

Scheme in a capability context
Comparison of Scheme and Caml
Poking at MzScheme
proposed error semantics
Dangerous eval
Sensory Scheme