The items you dig up from graves (other than amulets) seem to be purpose-built for researching -- they only require a shovel to acquire, and they give 80 research a piece. The only other use for them is to trade them for gold with the Pig King. Amulets, as of the Nov 27, 2012 update, provide resurrection upon death; amulets are probably too valuable to most players to exchange for research.

Tallbird eggs (cooked or uncooked) give 80 research as well, but fried tallbird eggs are a great food source -- if you have plenty of food and just want research points, this is a good option (and a better option than researching a bunch of other food to save the egg). Similarly, mandrakes give 100 research (also cooked or uncooked). These are quite rare. You can cook the mandrake to get the day-skipping effect and then use it to fuel research afterwards. Again, the sacrifice here is the very good food item, but if you have loads of food anyway, this isn't a terrible option.

Torches are a good renewable source of research points -- as far as I know, all crafted tools in the basic tier give 10 research points at 100% durability. Torches can be created with just straw and twigs, compared to the other tools which require you to use some of your flint (which is not a renewable resource).

Rope is a decent choice if all you have is grass, but torches are more efficient if you also have twigs.

If you have food to spare, cooked food gives more points than raw equivalents. Cooked monster meat is the first food I would sacrifice, at 7 points a piece, due to the negative effects of monster meat.

A (partial) list of items with research point values can be found on the wikia, although this doesn't indicate the worth of items in other aspects of the game.

To address the portion of the question about things you should never throw into the machine, I'd say never throw in any stone or flint (or anything created with stone or flint) because stone and flint aren't renewable in any way.

The diggable plants that you can harvest aren't renewable (although the resources you gather off of them are). Berry bushes (and possibly reeds) might be few enough and valuable enough that you wouldn't want to destroy them. Grass plants and saplings aren't renewable, but are common enough it wouldn't hurt to toss quite a few of them into the machine.

The Arqade question on renewable resources is a good place to start when trying to figure out what you should hoard rather than use for research.

Here's a handy list of the current known resources and their availability:

Renewable

• Grass
• Twigs
• Reeds
• Berries: infinitely renewable in the wild. If dug up and replanted, renewable but must be fertilized after every five berry harvests.
• Manure: infinitely available, as long as you have a herd of beefalo near you, or a pigmen village (feed them vegetables or flower petals), or a koalefant.
• Beefalos: renewable if a herd exists. Calves are born every autumn which add to the herd. Kill the last beefalo and it becomes extinct.
• Pigmen: generated indefinitely from their village or from pig houses. If the pig in a house is killed, the house generates a new pig in four days.
• Wood: renewable. Trees can be planted back from pine cones, unless you destroy the pine cones or burn the forest. Pro tip: dig up the tree stump to get one more log.
• Gold: renewable. Gold from gold-veined boulders don't respawn, but if you find a Pig King you can feed him meat (a renewable resource) or eggs (feed a bird in a cage monster meat to get them, or steal them from pengulls) or give him trinkets to get gold nuggets in return. Cave quakes can drop gold.
• Flowers: renewable. Flowers spawn butterflies which, when caught with a bug net and planted, yield more flowers
• Spiders: putting them in the resources because of the Silk. The nests generate new spiders when you kill them, up to their current limit (it should be 6 for the small nest, 9 for the medium and 12 for the big). If you kill all the spiders in a nest, they'll regenerate over time. If you destroy a tier 1 or 2 spider nest, you get spider silk but the nest is gone for good. But if you destroy a tier 3 spider nest (it has three lumps of web), you get six spider silk and one spider egg that can be planted to create a new spider nest. (The only way to increase the number of spider nests is to let a tier 3 nest become a Spider Queen; she leaves behind a tier 1 nest, walks around for a day or two, and then becomes another tier 1 nest.)
• Rabbits: they're regenerated as long as their holes are intact; if you dig up the hole, a rabbit comes out, but the hole is permanently destroyed
• Turkeys: they're vermin and they're there to gobble on your berries! Randomly generated in any bush, you don't have to worry about their quantity.
• Flint: Those that you pick up don't respawn anywhere else on the surface. They drop in caves on earthquakes;
• Rocks: Destroying a boulder or a stalagmite yields rocks, flint and occasionally gold, but boulders don't respawn. They drop in caves on earthquakes;
• Frogs: continuously generated from ponds. Frog Legs are also left when a Merm is killed.
• Fish: continuously generated from ponds. Fish are also left behind when a Merm is killed.
• Bees: continuously generated by beehives or bee boxes, up to a maximum of four per hive/box.
• All Farmable crops: your farms keep generating crops, needing the occasional (renewable) manure to fertilise the farm.
• Honey: You can get honey by killing bees (the bees will renew); or by creating bee boxes and then harvesting them periodically. (You can also get honey from destroying a beehive, but beehives don't appear to be renewable.)
• Mushrooms: They come back in a few days as long as you pick them. If you dig one, you'll get two at once but they'll never appear there again.

Not renewable

• Saplings - once they're gone (e.g. by being burned), they're gone. You can replant them anywhere, though.
• Berry Bushes - likewise. If you dig up a berry bush, you'll need to fertilize it when you plant it, and again periodically, to keep it producing berries.
• Grass Tufts - likewise. If you dig up a grass tuft, you'll need to fertilize it when you plant it, and again periodically, to keep it producing grass.
• Rabbit Holes - if you dig one up, it's gone forever
• Mushroom locations - if you dig one up, it's gone forever
• Honeycomb - you get one if you destroy a beehive, and you can use it to create a bee box. But it appears that the number of beehives you start with is all you get. You can also get honeycombs from killer bee hives.

As you can see, the list is still a work in progress, since I'm trying to discover everything on my own. I'll try to keep this updated every time I find something new. Keep in mind anyway that new features are constantly added to Don't Starve, so these information is not fixed and still likely to be changed from time to time.