Common Dravidian (esp Tamil, Telugu & Malayalam) word for "rectum".
Pedantically, Goodham (குதம் in Tamil script) refers specifically to the sheath inside the anal orifice & does not denote the anus or the buttocks. Strictly, the anus is distinguished by its own term, namely 'Goodoushtham'. However, 'Goodham' is often vulgarly & inaccurately extended to also mean "arse-hole" & even the whole "butt", which, in case of Dravidian women, often attains a pleasingly large size.
Since the same one Tamil letter is used to depict 'k' & 'g', & another is used for both 't' & 'd', variant dialectal pronunciations & spellings include: Kootham, Koottam, Kutam, Kotham, Kutham, Koothi, Gūdham, Gudam, Guddam, & Godham.
The word has entered Indo-Aryan languages, such as Magadhi or Pali: "gudaṁ, The anus. ... Ab.274." ('A Dictionary of the Pali Language' Robert Caesar Childers. London: Tru:bner, 1872-5, p.150) Of course, Sanskrit, one of the most highly Dravidianized Indo-Aryan tongues, has long adopted this term: "The lower end of the large intestine is called gudam (rectum) & this ends in gudoushtha (anus). The interior of the rectum is provided with three spiral grooves. These ring-like muscles lie a finger & a half apart from one another & are respectively known as pravāhini, visarjani & samvarani ..." ('Indian system of medicine'. History of Science & Technology in India, vol 4. O P Jaggi. Delhi: Atma Ram, 1986, p.114)
1) After he arrived in Madras, Sheikh Chilli was accosted by two big black Dravidian women. Thanking Allah, he followed them to a house in a lonely gullee, where they disrobed. But when he pulled down his pyjamas, they laughed as they pointed at his Ganges Worm. Then one locked his neck in a tight armpit headlock while the other took out a chilli & showed it to him. As she kept repeating "Goodham", the fool thought it was a name for "chilli" & she wanted him to repeat it. But the moment he did she disappeared & he soon felt the chilli being shoved into his anus. As he bit his tongue in pain, he knew he would never forget what "Goodham" really meant.
2) "kutam ... s. the backside; 2. the anus" ('Tamil & English Dictionary'. J P Fabricius. 4th ed. Tranquebar: Evangelical Lutheran Mission Pub House, 1972, p.259. cf tamilenglishdictionary.com)
3) The variants Koothi, Kootham & Kotham are derived from Gudham, as Darx notes: "Koothi, Kotham (derived from gudham) = anus" (darx 19 Jun 2006, comment on 'Get Your "Kundis" to the D.C. Meetup, 3/25' Anna. Sepia Mutiny (14 Mar 2006), sepiamutiny.com/sepia/archives/003147.html). This etymology is also provided in the Tamil Lexicon: "kutam, n. < guda. Anus." ('Tamil Lexicon'. Univ Of Madras. Madras: Univ Of Madras, 1924-36, p.990)
4) In Brahminical Kannadiga, one has the Sanskrit derivative: "guda. The anus; the rectum" ('A Kannada-English dictionary', Rev F Kittel, Mangalore: Basel Mission Book & Tract Depository, 1894, p.553)