Surviving Inferno Spiderlings in Act 1
Solution 1:
As a Wizard in Act 1 inferno I was using the Wave of Force ability with the rune to reduce cooldown/increase knockback force (Force Affinity). The issue as you point out with the Caves of Araneae is the small spiderlings are reasonably fast moving and frequently move in swarms, leaving you in the position where you're constantly running away.
However, they do die quite easily, so the best approach to ensure you have enough abilities to provide 'control' (Wave of Force, Frost Nova, that kind of ability) and enough abilities to get them down quickly. Keep alive by moving but don't go running through the level at top speed because you'll get surrounded.
Some elite packs combinations in inferno will will result in facepalms, but even a vortex/arcane enhanced pack isn't such a big deal if you can control their movement and you've kill all of the none-elites to reduce the amount of targets you're having to kite.
Solution 2:
Here are the things I'd recommend.
Make sure your skills are Inferno Capable. One of the biggest hurdles I had was ditching the skills I used up to that point in the game (Disintegrate, Electrocute, Force Wave, Frost Nova, etc.)
I'd suggest Hydra (Venom), Blizzard (Snowbound), Diamond Skin (Crystal Shell), Energy Armor (either Prismatic or Force Armor), Teleport (Wormhole), and a signature spell (Seeker Magic Missile for me.)
The idea is that you have two panic buttons: Teleport and Diamond Skin, which should let you get to safety against most uniques/champions. Blizzard and Hydra are your main damage sources, with Magic Missile getting thrown in whenever you don't have to run. Energy Armor helps reduce the amount of damage you take so a few hits from mobs don't kill you.Next, make sure your weapon is up to snuff. Try to get a 800+ DPS one-hander or a 1000+ DPS two-hander.
Now, when you're in the Arachnid Caverns, the best way to proceed is to systematically cast Blizzard ahead of you, with alternating patches. The idea is that if spiders begin to ambush you, you should be right next to a patch without having to cast a spell. Run through the patch, and when the spiders try to get to you, they'll all get slowed. If this isn't working well enough for you, you can go even slower, casting blizzard as a continuous path with no breaks between patches, or throw down a hydra every few patches as well. You should get used to this style, too - it works wonders later on as well, such as the sewers in Act 2.
Finally, take a look at your Resistances. Getting Resist All gear is one of the most important things you can do right now, especially if/when you go to Prismatic Armor. Think of it this way. Whatever % of damage your armor doesn't block, the resistances kick in. A resist of 100 means you'll be taking ~75% of that damage that gets through. Get the resist up to 300, and it's only ~50%. Aka, you'll be taking a full third less damage from every attack.
Hope that helps. Good luck!
Solution 3:
One obvious point is, try to walk in the middle of the path so you have some time to see any new mobs crawling up from the sides.Be aware of already cleared open or circular areas, so you know where to retreat and kite the mobs (well, what little kiting you can do in caves).
Are you playing alone or in a group? If alone, then do you take a follower with you? Both of these are factors in how to play.
In a group: Stay back and let the other team mates do the exploring, esp. any tanks like barb or monk (or any ranged who want to run ahead, they can take risks instead ;) ). You should still be within sight of the frontrunners, so that if some late spawns try to catch you they can quickly turn around to help.
Alone: Clear an area. Run ahead being very careful of any boss or elite mobs (don't get their attention), and then run back to the cleared area to AoE kill all the normal enemies that are chasing you. Warning: Unless you have really good dps this may not work well in Inferno.
With follower: Move slowly as your follower likes to attract elite mobs when you're trying to avoid them. Be aware of choke points if you're using Templar, as he can be a convenient human shield while you nuke from behind (though caverns paths are usually too big to block the little spiders :( )