What alien bits should I sell?

I've got a considerable amount of alien detritus lying around my base:

storages of assorted alien materials

Some items, like the damaged UFO flight computer, are marked as useless and intended for sale without consequence.

However, I have no idea how many bits of Alien Alloys I'm likely to need. Or what a stack of alien corpses might be useful for, for that matter. I could, however, immediately use some extra credits.

I'm tempted to sell a bunch of this stuff off to finance my near-term needs, but I'm concerned that some of this is going to be terribly valuable and rare later.

What bits of alien refuse are critical in the mid and late game, and how much should I keep on hand?

Do not sell alloys, elerium, or intact components. Alloys go into almost everything, elerium goes into lots of high-end awesome things, and stuff like Flight Computers go into the cool vehicles later. Damaged stuff is ok to sell, as you can't do anything with it. You will need lots of alloy and elerium, and there is never an amount of this stuff that is "too much" unless you are near end-game and your stores are overflowing in all the neat shiny end-game toys. And even then you probably shouldn't sell this stuff. How many high-end craft you build is a matter of taste. But the high end craft will perform better than our "mundane" stuff, even without the awesome high-end munitions. Gun parts would also fit here. Though if you can capture a lot of aliens you'll capture a lot of alien tech intact. You'll likely have to build some high-tech weapons on your own at some point, though.
In addition to that, you pretty much need 1 of everything for research, but you knew that already. Some items might be marked as having no research value, you can sell those. I'm pretty sure (Damaged) items are thusly marked, in fact. It may be these are the only items like that. The items will be marked as having "no research value/safe to sell" in the grey market sell screen, when you select them (it will be so marked in the description). As Kotekzot notes, you can also safely sell alien entertainment, surgery, and stasis tanks. I think I've seen all there is to see and I can't recall anything else that's safe to sell off hand.
Corpses can be used in certain construction, e.g. Muton corpses for I think Titan Armor, and floaters are used for the dodge power up I think. Also, council requests will occasionally come in for corpses. I sell some but I like to keep a decent sized stack in reserve and I don't sell anything Muton or "worse". It's worth pointing out that council requests are uncommon, so saving all your corpses probably isn't going to pay off. Council requests will probably be of much greater value than selling the corpses, to be sure (I sold 6 light plasma rifles for $1500).
As of Enemy Within, you can get gene mods from autopsies, in addition to the existing research benefits.

By request, here are the things you can spend corpses on researching/building. The list is not yet complete as I can't check every price in my longest game as I've already done a bunch of it. I'll update as I track the rest of the items down.

Cost in corpses (yuck!) of various items

Outsider Shard - (1) Skeleton Key (but I'm not sure if you can sell these anyway).
Chrysalid - (4) chitin plating
Ethereal - (1) mind shield
Berserker - (1) combat stims
Floater - (3) dodge power up
Heavy Floater - (4) advanced repair, (2) Advanced Flight
Cyberdisk - (2) tracking power up, (2) Advanced Flight
Drone - (2) Drone Capture, (2) Advanced Flight
Sectoid - (3) aim power up, (4) Xeno-Biology
Sectopod - (2) advanced construction
Thin Man - (4) Improved Med Kit

New from Enemy Within:

Thin Man - (2) Gas Grenade
Chrysalid - (2) Needle Grenade
Seeker Wreck - (4) Ghost Grenade

Cost in components for various items

UFO Power Source - (1) Firestorm, (2) Elerium Power Generator.
UFO Flight Control - (2) Satellite nexus, (1) Firestorm, (2) Alien Nav Computer
Fusion Core - (1) Blaster Launchers

Try to be cautious when selling certain things.

Try your hardest not to sell alloys, elerium, or weapon fragments, as you'll need those to research and engineer weapons and armor. I've also noticed that with the addition of engineering purposes, certain corpses and wreckages tend to be requested from the countries that you support. Try not to sell the following corpses, as countries tend to offer you stuff you'll need to fight the aliens: