Time to plunk down my brain dump!
Generations
Generation 8.0: 1998-2000
Generation 8.5: 2001-02
Model year differences
Gen 8 Corollas received a facelift in model year 2001. Differences are new bumpers which also required changes to fenders, slightly larger and curved corners, change from single H4 bulbs to 9005+9006 for the headlights. Also new is an opening for factory fog lights, standard on S but not available for all other trims.
Maintenance items
Spark plugs
Non-VVT-i: NGK BKR5EKB-11/Denso K16TR11, optionally BKR5EKPB-11/PK16TR11 platinum
VVT-i: NGK BKR5EIX-11 iridium
Engine oil
3.4 litres of any recent 5W-30 engine oil. Mobil 1 synthetic is a known good match to the 1ZZ engine. I use it myself. With good maintenance, tall oil filter (below) and Mobil 1, 8 months/8000km oil changes is possible, even for older 98-99 Corollas.
Oil filter
Stock size: 90915-YZZF2, PH4967 (for cross reference only; for your car's sake don't run FRAM :lol
Tall size (stock on 2ZZ, but fits perfectly on 1ZZs): 90915-YZZF1 (Recommended),PH7317
Manual transaxle oil
Two quarts of API GL-4 or GL-5 75W-90 gear oil. Red Line MT-90 is recommended. Use a 24mm socket to open the drain and fill plugs.
ATF
Dexron III ATF. Dexron VI should also be compatible. See user manual for capacity. Drain and fill every 2 years is enough for most situations. Open drain plug with a 10mm hex head. Fill through the dipstick tube.
Coolant
5.8 litres of a 50/50 mixture of Toyota Red and distilled water. Get it from a dealer. Grocery store, drinking grade distilled water is sufficient. Do NOT use spring water.
Cleaning MAF
Only Corollas with VVT-i has it. When MAF gets dirty you will notice a drop in gas mileage; CEL may come on with code P0171. Unscrew MAF from airbox, spray electric contact cleaner on two wires, one exposed, one shielded, be sure to clean both wires.
Wheels and tires
Stock steelie weigh 18lbs each.
Stock tire size
S/LE/VE Touring (98-00): 185/65/14
VE/CE: 175/65/14
Same speedometer calibration is used for all Corollas. You can step up to 185/65/14 with impunity.
Most common wheels found at this size are 14x6" +38 offset.
15" size: 195/55/15. Most common wheel spec at this size is 15x6.5" +40.
Another common size is 195/50/15. Only recommended if your stock size is 175/65/14.
16" and 17" sizes: see above
Wiper blades
Stock size is 18" passenger side, 20" driver side. 19" passenger and 21" driver blades can be used, but the wiper will move slower.
Common mods
Front end conversion
8.0 gen Corollas can have a 8.5 gen front end installed. Details elsewhere in this thread. Once the conversion is done, factory fogs can be installed (see below).
Fog lights (Some additions by Cyberbilly)
Factory fog lights can be installed on an 8.5 gen, or an 8.0 gen with the 8.5 front end. In addition to installing the lights themselves, the turn signal stick on the steering column must be replaced with a turn signal stick off of an S model, which has the fog light switch built in. The Toyota part number for this stick is 84140-02080. Finally, a small relay (part number 90080-87010, same as another small, gray relay in that area) has to be installed to an orange socket near the flasher relay, located above driver side kick panel.
All 8.5s (only) are pre-wired for fogs, as well as the signal stalk with fog light switch. You have to run your own wires, including providing for the relay, on a 8.0 gen.
Without a front end conversion, the tallest fog lights you can fit through a 8.0 bumper without cutting anything is 1.5".
Rear end conversion
The only external difference between 8.0 and 8.5 is the backup light lens on the trunk, which is an easy swap. To do this swap without breaking anything you need a long reach needle nose pliers to remove three clips in addition to the 3 nuts.
A not so visible change is the emergency trunk release lever on inside of trunk lid.
Getting a Tachometer
Consider swapping in a factory gauge cluster with tachometer before even thinking about anything else. With two caveats this is plug and play.
Caveat 1: With the facelift some wiring to the gauge cluster was rearranged. 01-02 can use 98-00 clusters by swapping pins 2 and 3 in the blue plug; 98-00 cannot use unmodified 01-02 clusters.
Caveat 2: You must transfer the speedometer from your old gauge to retain odometer reading (and stay legal). This is held to the cluster only by 5 screws which doubles as electrical contacts.
With the tachometer you also gain an outside temperature readout, but a ambient temperature sensor is needed. Get it from the dealer. All gen8s are pre-wired for all these.
Recommended Intake upgrades
K&N drop-in filter, #33-2672
And a number of intakes mentioned elsewhere
Electrical mods
Battery is group 35.
A group 35 Optima Red is available, so is a rarer group 35 Optima Yellow, but there are questions about Optima's reliability. OTOH my factory Delco Freedom 55D23L, rated only for 310CCA, served for 9.5 years after rolling off Cambridge ON.
Horn upgrades
Two horns can be wired - there is no one way to do it.
ZZE110 only has one puny horn from factory. Favourite upgrades are two Hella Supertones. Fiamm Freeway Blaster is also an option. If you must have an air horn, try Stebel Nautilus Compact.
Power amenities
All gen8s are
only partly pre-wired for power mirrors. Additional wires and jacks are needed for each of the front doors.
In car entertainment
One single DIN slot under center vent, one double DIN slot below HVAC controls, usually taken up by a storage bin or box.
On a Prizm, there is one double DIN slot below HVAC controls occupied by the radio, located higher than in a Corolla.
Front speaker is 5.25", rear speaker is 6.5".
LED upgrades
There is no light failure sensor of any kind on 8th gens so LEDs for brake lights are plug and go. An LED-compatible flasher is required to use LEDs for turn signals - this is a flasher-specific thing. Load resistors are not recommended. Use CF13GL-02 from V-leds or superbrightleds.
Make sure the bulbs you use in CHMSL and front turn signals have LEDs that fire sideways.
Seat belt reminder conversion
There have been numerous reports of seat belt reminder failures on 8.0 gens caused by a contact inside the seat belt spool coming loose. 8.5s have this contact at the buckle and are immune from this problem.
I posted a conversion DIY on corolland and also corollacustomz.
EDIT:
Someone tried my fix and it works! 
(Includes link to the actual DIY on corolland)
Transmission Swaps
A245E->C59 swap
Manual swap is a major undertaking, but besides all the fun in driving a stick, if done right is worth it as it opens the door to a lot of advanced gas saving (read hypermiling) techniques. Not to mention the auto tranny cannot be flat towed. Axles are identical for all trannies.
Clutch pedal have 4 mounting points, 3 nuts and a bolt. One nut screw on a stud on cross brace, one bolt bolts to firewall. Neither points are present on an auto car.
Needs repinning connectors on VVT-i engines with 4-speed auto.
A131L to C59 should be same, if not a bit easier.
A131L->A245E swap
Needs repinning connectors on VVT-i engines. Should get ECU from same generation 4-speed auto car. You gain one more gear and improved highway mileage.
2ZZ-GE swap
Has been done. Fabrication is required, as is the 6-speed transmission that goes with it. 1ZZ and 2ZZ have different bellhousing patterns.
VVT-i
Gen 8 Corollas gained VVT-i in model year 2000. With VVT-i also comes the change to individual coil-on-plug setup which places one coil on top of each spark plug and use of iridium plugs. 98-99 use two ignition coils, firing two cylinders at a time.
VVT-i is more for emissions than performance, although VVT-i-equipped 1ZZ-FEs in ZZE110s are rated 5hp more at 125hp.
1ZZ-FEs have no fuel return line. Fuel pump and pressure regulator are all in the tank, which like the fuel filter in these cars is
not usually a maintenance item.