There's a lot of bicycle types which i don't really give a thought until i found this new enthusiasm towards cycling. They mainly are categorized into functions or sports in which they are featured:
Racing Bike - for racing purpose, mainly for speed. Light construction, stiff frame and aerodynamic. They include road bike (race bike), track bikes, cyclo-cross, Triathlon and also TT bikes
Commuter bike - for everyday use, kinda basikal tua or basikal with bakul. Normal or comfortable rider's body position. Gets rider from A to B. Touring bike also fall in this category.
MTB - broad tires, suspensions and commonly found everywhere in Malaysia. Subcategories are XC (cross country), DH (downhill) and freeride. Most bikes are found in the xtreme sports you watch in TV.
Tricks/BMX - for stunts, tricks and also racing. BMX is also famous in the extreme game.
Special/other bikes - folding bike, electric bike, tandem, tricycle, monocycle, trishaw et cetera.
Those are bikes that we usually see and can be easily categorized. There's a lot more bicycle types out there. Enjoy the cycling world.