Changheon-yu Taekwondo (ITF Taekwondo) students will generally practise 24 forms, whereas Kukki-won Taekwondo (WT Taekwondo) students will generally practise 17 forms.
In a broader sense, however – of ‘How many forms are there in all of Taekwondo?’, or even how many forms there are in a given style of Taekwondo – is a more complicated answer. It depends on which forms you count as ‘proper’ forms.
Most Changheon-yu Taekwondo students will learn a total of 24 forms (assuming they get to a high enough level of black belt to learn all of them). However, in the Changheon-yu style in total, there are 25 forms. A form called Juche replaced an earlier form called Kodang. However, around the world today, some Changheon-yu Taekwondo students learn Juche and some still learn Kodang. Thus in the style altogether, there are 25 forms. There is also the lost form of Unam, which could be considered a separate form, and thus there would be 26 forms in Changheon-yu.
There is a similar situation in Kukki-won Taekwondo. Most students learn the series of 8 Taeguk forms at colour belt, and then another 9 forms at black belt, starting with Koryo, making 17 forms. However, there is also the older series of 8 Palgwae forms, which were supposed to be replaced by the Taeguk forms, but which are still practised by some, and there are also the 10 new competition forms. These, combined with a few other incomplete or obscure forms in Kukki-won, mean that one could argue that there are about 38 forms in Kukki-won Taekwondo – not 17.
And then there are other styles of Taekwondo, such as Cheongdo-kwan Taekwondo, which have some distinct forms, and which if counted would increase the total number of forms in Taekwondo.
So the total number of forms in Taekwondo – either all of Taekwondo or one specific style – depends on which ones you want to include. The book Taekwondo Forms lists 71 forms from four different styles of Taekwondo, thus the total number of forms in all of Taekwondo is at least 71.
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If you'd like to learn more about the forms / patterns in Taekwondo, consider buying this book: Taekwondo Forms. It lists the movements and gives the floor diagrams and interpretations for 71 forms from four different styles of Taekwondo - it's the ultimate reference book for anyone studying forms in detail.