To my knowledge, 1&1 offers domain regs for $1 but renewals are more expensive.
EDIT: only if you're American; I tried. If you're not, the prices are regular.
That's pretty much it. You can't reg domains for $1 without a catch. You can use a godaddy coupon and it will give you 1 domain for $1.
There's a running discount on dynadot where com domains are $6.99 a piece. That's the best you will get.