I've gone to several bouts of muay thai and what fascinates me the most is the ritual surrounding the event. The two fighters enter the ring and, for about 5-6 minutes, each dances/prances around the ring in some ritualistic fashion (which I presume is essentially some prayer to the boxing gods to get them through the bout safely). Actually, it's called the Wai khru ram muay and Wikopedia describes it as follows:
Wai khru ram muay (Thai: ไหว้ครูรำมวย) is an action of respect in Thai culture that is performed by participants in Muay Thai competitions. Wai is an action of Thais to show respect to others by putting the hands together like in prayer. Khru means teacher. Ram means dance in the old Thai traditional style. Muay means boxing. Usually Thais prefer to call it short Ram Muay or Wai Khru. Ram Muay is the way to show respect to the teachers and the trainers. Also, in past muay Thai was usually fought in front of the king, so Ram Muay was also to apologize to the King for the brutality in fighting.
The fighter first performs the Wai Khru, circling the ring three times before kneeling and bowing three times as a sign of respect to God and man. He also bows to Buddha to ask for protection for himself and his opponent and for an honourable fight.
The fighter then performs the Ram Muay, whose simple movements demonstrate a fighter's control and style. Each fighter performs the Ram Muay on each side of the ring to demonstrate his prowess to the audience. The Ram Muay is a personal ritual, ranging from the very complex to the very simple, and often contains clues about who trained the fighter and where the fighter is from.
The practitioner may wear a headband called a Mong Kon and armbands known as Pra Jiad during the ceremony, and the Ram Muay may be accompanied by music. The Mong Kon is unique to Thai boxing and not worn in Cambodia or Burma.
I've only attended the bouts at Lumpini once and it's a great experience for muay thai fans. Besides the higher quality of participants, you also get a chance to see the rather animated betting going on up in the cheap (upper) seats.