I will be on vacation in Tenerife in September and plan on hiking to the top of Mount Teide. I know only 200 people per day are allowed to hike to the summit and that you must obtain a permit. My question is, do people taking the cable car to La Rambleta get preference over those who hike the entire way? Any other tips would be most welcome.

You need to get your permit before you start your hike. Nowadays you can obtain it here:
https://www.reservasparquesnacionales.e ... 2&act=%201

Once you have it and start during the requested timeframe, they will let you get to the top. If you're far out of the timeframe or don't have a permit, you won't get to the summit. Regardless of how you got there.

Bot it looks like the permits for September are already taken

Wow!!! Even October is fully booked. It looks like I may have to book for next year.

Back in 2008 there was an easy solution around the permit requirement: if you spend the night in the refuge high up on Teide, you were allowed to go to the summit early in the morning, before the cable car would start running. I don't know if that's still the case, but it shouldn't be hard to find out.

I decided to go to the Canary Islands on short notice (see Teide, here I come!), and with just one phone call I got a reservation for the refuge. And the early morning ascent comes with a great bonus: provided that the weather is good, you may experience the sunrise from the top, and the iconic shadow of Teide on the other side:

Thanks for the info, I will try and see what happens.

Hehe, another option is to go on a "serious" holiday. We had a permit for Jan 1st but didn't need it as the cableway was closed and no ranger to be seen. We also did a permitles attempt on Dec 31st a few years previously but were headed off.