Sturdy earbuds under $100

Research head-fi.org forum and their ads as well.

First off, I can't believe anyone listens to those Apple earbuds at all. They're horrible sounding and physically hurt my ears when they're in. Just awful.

Anyway, I've got Sennheiser CX500Bs that are MUCH better and more comfortable than the Apple garbage. I've had them for years and they're still going strong, and they also incorporate a volume control on the cable which sometimes comes in handy. If you can find them (not sure they're still making them) you can probably get them for about $40, but make sure you get them from an authorized dealer because there are fakes out there that are tough to spot. They also offer the CX300B that looks very similar but lacks the volume control and can be had in the low $30. Not sure of how they sound vs. the CX500Bs though, but I'm sure they still sound a helluva lot better than the Apple buds. They both also come with a few different sized ear adaptors so you'll get a good, comfortable fit that will also minimize any sound leaking out that others could hear. I'd categorize the sound of the CX500Bs as nicely detailed and a bit on the warm side due to warm, punchy bass and rich midbass frequencies. These might be a good choice if you listen to a lot of music that's not well recorded or thin/bright sounding.

Probably some of the best 'phones in the sub-$100 price range are the NuForce headphones (see their website). This is a high-end audio company that makes quality stuff. I got their NE700M 'phones as a gift for a friend and he likes them a lot. The buds are actually made from machined aluminum rather than plastic, so they'll probably hold up better than most. Probably not as warm sounding as the Sennheisers but probably more neutral and detailed, although I've not heard them. They're $69, but they also offer models at $65, $49, and $25. Can't see you going wrong with these, but unlike the Sennheiser's they probably won't do much if anything to help bad recordings sound more listenable but good recordings will probably sound even better.

As mentioned above, read up on what else is out there but these are at least two options I have first-hand experience with. Best of luck and congrats on getting rid of those horrible Apple 'phones.

Research the Yuin PK2. Fantastic ear buds that don't require an amp, for $80.

As far as durability...you need to take 30 seconds and take care of them. I bought the Sony MDR-E828LP Fontopia Earbuds with Winding Case off Amazon ($10), just for the case. 20 seconds to wind them into the case, and they are safe and sound under whatever you dump on them. :-)

Mot

Etymotics, whatever their cheap one is now. Great sound, and the in-ear design makes them also isolating, which means less volume for a given piece of music.

I have a set of the ER-6, which was the sub-$100 model a few years back. Great phones if they fit you. Some people don't like in-ear headphones.

I've been using Etymotic ER6i for about 6 years or so now. They didn't seem overly indestructible when I got them, but I've been on the road with them, worked out in them, and so on without any hiccups.

They're discontinued, but I think the current Etys are made just as good. I have the ER6i and ER4S and both sound great. They isolate very well. I don't think they're the safest things to be wearing while on the go, but if you're sitting in a library, on the train, etc, no problems.

In ear monitors take a bit of getting used to, but most people don't mind them. I didn't like the way they felt the first few times, but they're fine now.

I think the hf5 is about $80 or so.

I have tried a few and like the Sennheiser CX300II very much in this price range,

Westone UM1 in-ear monitors. The best available in that price range. Best customer service in the world as well. They are one of the very few companies that truly cares about their customers and wants them to be completely satisfied with their product.

If you are listening to a turntable, it indicates that you are not moving around or doing portable listening. Why not invest in a decent set of headphones? Look at the Audio-Technica ATH-M50 if you want a set of headphones that seal well so nobody else can listen to your recordings.

Apple earbuds are rank. I would pay Apple $5 to not include them in the packaging. Just the worst POS ever made.

Grado, $89 new, sound very good. Don't know about indestructability, but you can break anything if you really want to. Midrange is especially excellent, as always with Grado.

I won't comment on any particular brand of ear bud, because I use many different ones. I will say that you can get decent ones for around $50 from places like bestbuy or your area equivalent. What I've been doing is to buy a set that I like and then get the accidental damage warranty on them. This has proven to be a very good way to go, especially for my son. $100 can keep you in buds for a long time, if you exercise any sort of care with them.

Etymotics are the real deal. Not only are they the most accurate earbuds you can buy they are also the toughest. There are kevlar fibers in the wire. You can hang yourself with these earbuds. If you somehow manage to break them the company will sell you a new set for 1/2 price. 
I use ER4 XR's for serious listening and an old set of ER 5's for the gym, lawn mowing and in the shop. They are 10 years old! Etymotics have a 31 dB attenuation rate which makes them quieter than any ear protection you can buy that I know of. 
One word. These earbuds fit into your ear canal with three seals. The seals are very soft rubber but initially they may be sort of annoying. You get use to them over several weeks and eventually you even forget they are there. But, when you hear them it will be a real eye opener. Because they are tuned to operate within the ear canal they are more accurate than any electrostatic headphone out there. Also,they do not weigh your head down like headphones and your ears do not get sweaty.