I wrote this kind of quickly, so I'm not going to bother with too much of an introduction. I've read at least one other suggestion that had a few good things (I believe webbed, hanging corpses was one of them), but here I'll just be listing some of my ideas for improving spiders.
Spiders are pretty good as they currently are in terms of look and abilities, so I'll just be suggesting some new stuff.
Mordor spiders would be removed. There would just be the Mirkwood spiders (which would just be called "Spiders", or maybe "Great Spiders"), which would now also spawn in Nan Ungol and the Mordor mountains. However, Great Spiders would be able to reach the size of the biggest Mordor spiders, which are currently slightly bigger than the current Mirkwooders.
Spiders would be repelled by bright blocks, like Edhelmir, Durnaur, etc. But they'd be attracted to smaller sources (torches, fires, etc.). When a spider gets close to one of these, they'd break (eat) the light source. Obviously, torches within protected territory would be safe from this. Every once in a while, they should place down normal webs that will despawn after a while.
Spiders will no longer act friendly to Orcs (say goodbye to Orc spider-riders). Instead, they will actively attack them, along with every other creature in the mod. Players can also be attacked by spiders, but can befriend them by feeding them Man-flesh. They can't be ridden, but there's still a way to get spider-mounts. (Note: Spiders of any kind can only be fed Man-flesh by players with +200 Mordor or Dol Guldur alignment.)
The ability to breed evil mounts has been needed for a while. The Wargs especially could use this, but this suggestion focuses on the creepy-crawlies.
When a grown spider is fed Man-flesh, or when they kill something, they'd be able to breed. This wouldn't require other spiders in the area, just the one - plus any web (not including the temporary placed ones). The spider would move near the web, and place a new item on the side of the block called a Web Sack. Just look at a spider's egg sack in real life if you want to know what it should look like.
Eventually, the sack would break, spawning 1-4 Spiderlings. Baby spiders resemble very, very small spiders, with dull eyes and stubby legs. These would have very low health, being able to be killed in a single hit. After a while, these would grow into full adult spiders. All these spider-children would grow into the normal black variant. You can right click the Web Sack with gulduril to breed the green variant, and with a bone to get the blue. Spiderlings wouldn't be able to attack or deal poison/slowness until they reach adulthood.
Right-clicking a web sack with a piece of Man-flesh will make the spiders that hatch form a bond with you. They'll even allow you to ride them, if they're the right size. This is the only way (outside of commands) to get spider mounts.
This special variant only spawns in nests in the Mordor Mountains. These are incredibly large and strong (about twice the size of the largest spiders), with a light venom in their bite. The Gloom-weavers will attack anyone, except players they've made deals with (see below). Be very careful, for these great spiders have 12 points of armour on top of their 45 health points, and can deal 4 points of damage to unarmoured players, plus their poisonous bite. Luckily for good players, these cannot be ridden. For a good idea of what these fell beasts would look like, take a look at this book-based design of Shelob , and imagine it not nearly as big or bloated, with smaller horns and less hairs.
Not so much "taming" as it is reaching a compromise. The Gloom-weaver must be fed up to half a stack of Man-flesh to trust you. It won't follow you or allow you to ride it, but it would no longer attack you, and you can now begin breeding spiders from it. Furthermore, it would allow you to hire lesser spiders from it (not with money. Man-flesh, as always.), and all nearby spiders will become docile to you. It will also speak, since giant Spiders can speak. Hired spiders are automatically friendly to you, and can be ridden.
Successfully "taming" a Gloom-weaver earns you the achievement Glut of Life. Hiring a spider from a Gloom-weaver earns you Ghastly Brood.
Gloom-weavers are bred quite a bit differently to normal spiders. A Gloom-weaver, after killing another mob or being fed a good deal of Man-flesh, will seek out another, smaller spider. After mating with the other spider (who will die), they'll attach a web sack to their web like normal. This will only produce normal spiderlings, unless the player intervenes. Right-clicking the Gloom-weaver's web sack with Man-flesh will cause the sack to swell a bit. Keep doing this until the sack is the size of a block, and when the spiderling hatches, it will come out as a small (still quite large) Gloom-weaver. It will grow naturally over time, but will attack players once it reaches its full size. A player can continue to feed a newly-born Gloom-weaver Man-flesh. Each time this is done, the spider will grow bigger. When it reaches its full size from being fed, it won't attack the player. This is the only way to really, permanently, "tame" a Gloom-weaver.
These nests spawn throughout the Mordor mountains and Mirkwood, especially Dol Guldur. Choked thick with webs and hanging strings, these dens are littered with skulls and waste blocks. Very dangerous places, not least because of the Gloom-weaver that may be waiting inside. Dens in Mirkwood would be large, shallow pits between trees, while those in Mordor would be large caves. Both are full of Spiderlings and grown Spiders, and Gloom-weavers may spawn in the Mordor variants.
Because Orcs would no longer be friends with spiders, these pits don't really make sense. So I'll suggest some changes to them. These used to be Warg pits, but are now ruined. The bricks would be cracked and the wool frayed, the chests empty except for rotten meat and the bones of Orcs and Wargs. Spiders, long ago, crept their way out of their dens, and digging through the stone into these pits, devoured the wolves and goblins, and made their nests there. Waste blocks, skulls, and webs would fill the area. One of the walls would have a large crack in its wall, connected to the main spider nest, filled with even more webs, waste, and skulls.
Webs - Walking into a web (and a web of Ungoliant) will attract any nearby spiders. Spiders will place webs every once in a while, though they don't last long.
Web of Ungoliant - Gloom-weavers temporarily place these in place of normal webs. If possible, they'll also now produce a darkness effect, lowering the light level around them. Walking into one effects a player with blindness for a short period. They should spawn much more rarely outside of Gloom-weaver dens to balance this.
Web Sack - Placed by breeding spiders. Has no function other than spawning Spiderlings after a while. Won't yield an item if broken.
Web String - These hang from the ceiling like Orc Chains, and have a lesser slowing effect to webs. Crafted two string above a slimeball on a Mordor or Dol Guldur crafting table produces four web strings. They can also be combined with bottles of poison to induce a very light poison effect on whoever walks through them. Spiders can also climb up these.