Here are some (not many, yet) references for topics discussed in the 
seminar. Feel free to suggest more! In particular, speakers are requested
to include some references with their talks.

Weil conjectures and Weil cohomologies: Appendix C of Hartshorne, Algebraic
Geometry, is a great place to start.

Etale cohomology: Milne's notes on Etale Cohomology (www.jmilne.org), and his
book Etale Cohomology (may be a bit dry for beginners); Freitag and Kiehl, 
Etale Cohomology and the Weil Conjectures; Tamme, Introduction to Etale 
Cohomology; Deligne et al, SGA 4 1/2 (much more readable than SGA proper).

Sites and Grothendieck topologies: If you really want to get this from the
source, try SGA 4-1. But you might want to start with one of the etale
cohomology references.

Cohomology of complete intersections: Griffiths, On the periods of
certain rational integrals I, II, III.

Algebraic de Rham cohomology: Grothendieck's and Hartshorne's IHES articles,
both called "On the de Rham cohomology of algebraic varieties".

p-adic Hodge theory: Berger, An introduction to the theory of p-adic
representations (arXiv, math.NT/0210184).