· condoms that prevent disease (sheepskin condoms are okay as contraceptives but are not considered safe against hiv)
· transparent flexible medical feeding tubes
· disposable scalpels
· disposable pipette tips, crucial for biology work
· catheters (one company does make them from a bioplastic but it's still a plastic)
· i was going to say 'printed circuit boards' but it turns out that some of them are made out of sapphire instead. so i guess i'm limited to 'impact-resistant printed circuit boards'
· communications satellites (they'd've weighed too much to launch without much larger rockets, and they'd also break during launch)
· cell phones
· playground slides that don't cause burns when it's sunny
· spray foam insulation
· permanent markers (the ink is a plastic)
· bulletproof vests (plastics are the only materials with the necessary combination of strength and lightness)
· landfill liners
· magnetic tape
· photographic film, as opposed to glass plates, and therefore pocket cameras and motion pictures
· pneumatic tires, and therefore bicycles and automobiles that can go faster than a walking pace
· insulating panels for houses
· garbage bags
· breast implants
· adhesive tapes, including duct tape, scotch tape, packing tape, and masking tape (pressure-sensitive adhesives are plastics)
· band-aids
· lcds (the liquid crystals are a plastic, just one that's molten at room temperature; the polarizing filters are also a plastic, a solid one, although conceivably you could find a way to use wollaston prisms for this instead)
· ion-selective electrolysis membranes (nafion, etc.)
· phonograph records. if you're unwilling to consider shellac a 'plastic', even though it's a moldable thermoplastic organic polymer, this can be restricted to 33rpm and 45rpm phonograph records
· compact discs, probably. although you could surely micro-etch a surface to store digital data without plastic, the stamping process crucially depends on plastic's ability to mold to submicron precision as a way to mass-produce the resulting shape
· hologram stickers, similarly
· baby bottles. the nipples are plastic (rubber, a plastic, is the only natural material that will work) and if you make the bottle itself out of glass, the baby will break it
· flexible electrical wires that don't short out if they get wet, I think. you can't insulate flexible wires with glass or porcelain. certainly insulating wires with cloth (silk for small wires) was commonplace in the early 20th century, and although you can get wires insulated with an layer of ceramic so thin it's flexible, i don't think it's flexible enough or abrasion-resistant enough for household use
those are things you can't make at all without plastics. in most other cases, you could make do: by molding things out of beeswax or glass, stamping them out of steel, carving them out of wood, machining them out of brass or mykroy/mycalex (if you don't consider that a 'plastic'), molding them out of plaster, using decay-prone natural fibers instead of stable plastic ones, painting cotton cloth with linseed oil, oxidatively cross-linking linseed oil or urushi as a binder for other uses, sintering sapphire, or bolting together pieces of porcelain or granite that had been ground to shape
that would work for clothing, camping, rock climbing, sailing, electronic components, paints, electrical equipment, automobiles, and most industrial processes. but not for the bullet list above
however, even in those cases, the resulting products would in most cases be orders of magnitude more expensive, so the aspect of modern life that would be missing would be that non-wealthy people have access to them. they would also be much shorter-lived in most cases because they would rot and break more easily