In terms of changed gameplay, by far the biggest impact is on the early game. Summon magic takes the place of attack spells nicely... actually, I wound up having Aeris kill darn near everything with Choco/Mog? from the time I got it until she got her Level 4 limit break (at which point other materia combos were available), and Enemy Skill has most of the support spells a party might desire, from White Wind (curative) to Big Guard (protect/haste), to Beta/Trine/Aqualung/Matra Magic (cheaper hit-all spells). By the time I hit disc 2, the game was not significantly different from the standard one.
In terms of sheer annoyance, probably the worst fight in the game was the one in the elevators in the Shinra building early on in Disc 1; no summons or enemy skills are available, and the bosses are at long range, which leaves only Barret with a functional attack (Red XIII can use his limit break, which is small consolation). At least Aeris has Healing Wind...
Emerald Weapon is not significantly harder than with green materia--the only spell that I particularly missed was Ultima (or any other repeatable high-damage spell) for taking out the eyes. It wasn't terribly necessary in any case (I don't recall if Emerald did Aire Tam Storm at any point; I know I didn't use all of my stars on Final Attack + Phoenix).
Ruby may not be significantly harder, either, but she's darn well hard enough as it is...
EvilSouthie has played through the game only equipping one Restore materia (never used, I was just paranoid), and some All materia (used for cash). The Yuffie sidequest is just plain amusing. Buying the assorted elemental damaging items is a must, if only for the random monsters that are immune to physical. In addition to the painful elevator fight above, the winged-snaked thingie on the beach is horrible (also long range). Abusing the various healing limit breaks is extremely useful, and playing with hypered Aeris+Yuffie for most of Disc 1 will definitely show you why the spoiler happens.
Notes: When fighting Lost Number, use an elemental item to finish off the first form, then pound it with several limit breaks at once. Right before getting the sub there's a crane boss fight that I never remembered when playing through normally, but it kicked my butt repeatedly. Having a shifted Vincent as your only living member is not so much fun. He's extremely useful for most of the endgame, but for that fight I found other characters to be more useful. You can actually take on the Pagoda Gods sidequest with Yuffie as soon as you get there even with this challenge, although it's difficult enough that you might want to wait for a little bit. I seem to recall burning the last boss out of mp, and not through the cheesy magic hammer technique.
I didn't try fighting Emerald or Ruby, as I hadn't ever tried it with materia and wouldn't know what to expect.
Not having any materia will make one of Emerald's attacks much less potent, but OTOH you'll have to deal with the timer (since you can't use Underwater). It's probably still possible to rack up sufficient damage in that time, but it would require a goodly chunk of limit breaks. You'd want an assload of Megalixirs as well, since there's no good way to shrug off a Revenge Stamp.
DanCicio's thoughts on his partially-completed "no materia" run:
The fact that this works makes me sad. Whenever not absolutely essential, I use no magic whatsoever--including elemental items. (I do keep all of my Alls equipped, in case I'm ever short on cash, but using only 3 characters frees up a ton--haven't sold a single All yet and I still have assloads of gil.) If memory serves, the only time I've used the items so far is on Lost Number, and that's because Vincent is one of my standard party members so I wanted to get him. I'm just starting disc 3 and haven't had a lick of trouble since.....well, ever, I think. Even Hojo at the end of disc 2 with his reviving monsters was a waste of time.
My party consists of Cloud, Red XIII, and Vincent (always--I think it's best to just focus on leveling 3 characters, particularly with this challenge). I picked Red XIII because he gets the "memento of father" item early and is thus has overpowered attacks for a while, and thus winds up leveling his limit breaks quickly. I use Vincent because ranged attacks (and, relatedly, taking half damage) are important, plus his limits can be useful (mostly for extra HP, though--I *do* miss HP-Up materia, but it's far from necessary). The thing that I think makes it all work best is giving Vincent a Fury Ring. Since all they're doing is attacking anyway, one of them might as well be berserked, and it should be the one with the sketchy limits. In fact, the most difficult aspect of the entire run (by far) has been remembering to unequip the Fury Ring before significant plot battles.
Oh, yes, and hypering.....TOTALLY BROKEN. *ahem* Sorry, just wanted to point that out. (Now, it's not like it isn't broken in a standard run--it's just far more obscene with this challenge in effect.)
One thing that I expect to be necessary before trekking down into the crater is whoring the Wutai area for X-Potions. Other than that, I'm planning on running at Sephiroth fairly soon. Sadly, I don't expect the Gelnika to be anywhere near reasonable for a long time--not being able to Added Effect my armor to avoid confusion and the like is just too painful.
Notes after completion:
Damn, Sephiroth is a pansy. Almost as much of one as Jenova. On a whim, I descended into the crater without preparing at level 58. I made it to Sephiroth but didn't have quite enough healing items to take him down--though I made him earn his victory after about 40 minutes and 5 Super Novas (Novae?). After that, I went and whored Wutai until I had 99 X-Potions, as well as maxing out a bunch of other healing/support items. That put me at level 61, and I pretty much walked through the crater (fleeing from Tonberries, sadly, always wishing I could morph them into Ribbons at will) and bitchslapped Sephiroth. It still took a while, but he couldn't kill my party members faster than I could revive them.
Oh, quick aside--can you morph bosses? If so, what do you get for morphing Sephiroth (or the Weapons)? Just curious; maybe I'll try on an old save file.
For equipment for the final battle: Cloud--Ultimate Weapon, Mystile, Ribbon; Red XIII--Limited Moon, Mystile, Reflect Ring; Vincent--(insert name of ultimate weapon here), Bolt Armlet, Water Ring. Now, the Reflect Ring was a beautiful thing, though mostly irrelevant; I think I reflected one Shadow Flare that would've wiped the floor with Red XIII and instead did 2500 damage to a Walled Sephiroth. Those Mystiles, though..... Other than Shadow Flare, the only attack of Sephiroth's that routinely killed a party member at full hit points (a little over 5000) was his standard attack--which now misses two of my party members (the effective fighters) about 50% of the time. Now *THAT* I like! =o]
I didn't attempt either of the weapons, but at some point, I may. I really really hope that I need to level more, though, or else it'll just be far too sad for words.