Below is a list of pronouns meaning 'I/Me' in Thai, in approximate order of how common they are in everyday speech. Although there is a great range of pronouns, they're actually used quite sparingly and often omitted unless it's absolutely necessary to convey the meaning. For instance, to say 'Where are you going ?' in Thai is just bpai nai (literally 'go where ?') - no pronoun necessary.
Though this list may seem pretty intimidating, you can get by perfectly fine in almost any situation you are likely to come across by knowing only chan, pom and di-chan.
chan
ฉัน
This is most common word used by women, and can be used in any situation that's not especially formal. Men can use chan also, but it's much less common and is only used very informally. In Thai love songs sung by men, for instance, they always use chan to refer to themselves.
pom
ผม
This is the normal word for "I / Me" used by men, which can safely be used at pretty much anytime talking to anybody. When talking to friends though, a less formal word is likely to be used instead.
di-chan
ดิฉัน
This is used only by women. It's a safe word to use for most situation but is quite formal, so it's unlikely to be used when talking with friends.
pee
พี่
Literally meaning "older brother / sister", this is quite a common word that can be used for 'I' when you speaking to someone younger than you. .
norng
น้อง
The opposite of pee, this means "younger brother / sister". and can be used to mean 'I' when talking to people older than you.
This is another word used only by men, and it's used to show respect when talking to people perceived to be of 'higher status' than you. For instance, the porter in an expensive hotel might say it when talking to a hotel guest.
rao
เรา
Confusingly, this is the normal word for 'we/us' but it is also used by both men and women as an informal word for 'I/me'.
goo
กู
This is sometimes used by Thais when talking with close friends. In almost any other context (even a husband/wife conversation), it is offensive and only used as an insult to the listener. As a foreigner, you're better off avoiding it altogether. When used, it's almost always combined with meung which is a similarly offensive word for 'you'.
noo
หนู
Literally meaning 'mouse', this is used by women when speaking to people much older. For instance, a Thai women talking to her parents will often say it. It can also be used as a word for 'you', 'him', 'her' etc if talking to/about a young child.
ua
อั้ว
This is a word used only by Chinese Thais.
dtai-tao
ใต้เท้า
Literally meaning 'under your feet', this is a respectful word similar to gra-pom.
kah-pa-jao
ข้าพเจ้า
This is a very formal word for 'I/Me' that is almost never heard in normal speech, but can be found written occasionally. For instance, when you have to sign an immigration form to enter Thailand, the declaration in Thai uses kah-pa-jao as the word for 'I'.
kah-pa-pra-put-ta-jao
ข้าพพระพุทธเจ้า
This is a Royal Thai word, and is only used by those in conversation with the Thai King or another member of the Royal Family. That being the case, it's not a word you're likely to hear often, except at the cinema where it's the first word of the royal anthem played before every film. Literally translated, it means 'The servant of the Lord Buddha.'
Be warned that if you say this word in the wrong context, it may be taken as mocking the royal family and could land you in trouble.
This is not a definitive list of words (some sections of society e.g. royalty and the military have their own words that only they use, and family relationship terms are also often used as pronouns), but it includes most of the main ones.
One of the most common ways for women to speak about themselves isn't listed though, which is the habit of using their first name instead of any pronoun and so speak about themselves in the third person. Though men can do this also, it's not very common and sounds a bit effeminate so it's not a good habit to get in to.
Another common way of speaking is by referring to your position or title instead of using a pronoun. For instance, a teacher talking to his students may use a-jahn (meaning 'teacher') as a word for 'I/Me' instead of one of the pronouns above.
