This is a commonly asked question so many curious teachers  want to know. A cut and dried answer is really not available. The truth is the answer is complex and has many angles.
The answer is ....Yes and no. Teachers of English as a Second Language (ESL) are always in great demand in Taiwan. With more than a thousand schools in the Taipei area alone, it is relatively easy to find work. For ESL job ads, look in the classified sections. There are many schools who need a teacher bad, sp will hire any teacher, with or without a proper degree or going through the proper process without a work visa, with little fear of getting caught. 
In the old days you could work illegally, However, those days are generally gone. The Taiwan government system has tightened up a whole lot in the last decade . Basically you must have a work visa. The only way you can get a work visa is to be sponsored by the school  that wants to hire you for one. Simple as that. Find a school needing an English teacher, and then they will  sponsor you and get the ball rolling for applying for an ARC. To do that, you need a BA. DEGREE , it's basically that simple.

We  still get many emails asking questions such as these

"Will I get caught if I work illegally"

Answer: It's always a chance, but a few percentage get caught as teachers are still needed here and usually you just get kicked out of Taiwan

' or.....

I am very interested and motivated to come to Taiwan to teach English. I already booked my flight for the new school year ! I just want your opinion of how difficult will it be for me to find a good teaching position without a proper degree?

Answer:

You can find a position easier if you are already here, but better to get a PT position at least, before flying over.

Post ur cover letter in the classifieds

Or " I have had a few friends teach in Taiwan years ago without a bachelors degree, is it still that easy acceptable?"

Answer: It is much harder than years ago as mentioned above.

I DO KNOW MANY PEOPLE WHO HAVE WORKED  here in Taiwan for ten years and never got an ARC. They overstay or normally take a visa run every 2 months. Don't be silly and take the chance if you have other options !Get your degree first. Most people who don't have degrees don't do AS well as the teachers doing it the legal way. Howeve. they have saved a little in taxes. Another thing you may want to keep in mind is that Taiwan  has a tendency to  reel or suck you in and you will get attached. You will all of a sudden wake up one morning realizing that  ten years of your life  have gone by , and you  still have no proper degree and no future in teaching anymore. 

...and like this one, from a guy who doesn't want to do anything "shady," but intends to use a fake degree when he comes to Taiwan to teach: I would like to work there and so would a fake degree be alright to use for getting the work permit as I don't really want to work illegally or do anything shady.

Thats a little bit like an oximoron...No?

For Canadians:

To work legally in Taiwan you must have a resident visa that specifically states you are permitted to accept employment. (See "Visa Matters.")

The Canadian Trade Office cannot become involved in any case, conduct an investigation, or act as lawyer or mediator in any personal, legal or contractual conflicts experienced by Canadian citizens. It cannot investigate, certify or vouch for prospective employers. It is up to each individual to evaluate any employment offer before signing a contract.

The currency in Taiwan is the new Taiwan dollar (NT). For the current exchange rate, visit the Bank of Canada website.

If you encounter difficulties while teaching English in Taiwan, contact the Canadian Trade Office in Taipei:

5F & 6F, Hua-Hsin (Citibank Building), No. 1 SongZhi Road, Xinyi District, Taipei 11047, Taiwan
Tel.: 886 (2) 8723-3000
Fax: 886 (2) 8723-3590
E-mail: tapei@international.gc.ca 
Internet: www.canada.org.tw

Office hours: Monday to Friday, 8:30 a.m. to 5:00 p.m.
Nearest subway station: Chung Shan Middle School (first stop on the Mucha line)

For emergency assistance after hours, call the Canadian Trade Office in Taipei and follow the recorded instructions. You may also call Consular Services, Foreign Affairs and International Trade Canada, in Ottawa toll-free at 00-800-2326-6831 or collect at(613) 996-8885.