There have been several bands with this name.
1) The best-known was a garage rock band formed during 1963 in Ann Arbor, Michigan whose drummer was later to become Iggy Pop, who later left to form The Stooges. They had a minor hit with "Again & Again".
2) At least one more American 1960s garage band with the name The Iguanas, presumably from Baytown, Texas. Unlike the better-known Iguanas, they had a single released during their existence.
3) The Iguanas from New Orleans, Louisiana, formed in 1989; their music reflects the local mix of Latin/Caribeño rhythms and themes with distinctive jazz and R&B elements. Their long-standing line-up includes René Coman (bass, piano, organ, guitar, mellotron, background vocals, tamborine), Joe Cabral (vocals, sax, bajo sexto, guitar, organ, percussion), Doug Garrison (drums, percussion), and Rod Hodges (vocals, guitar, accordion, lap steel). The band, one of New Orleans's favorites, has a string of melodic albums and a respectable and wide-spread fan base. Their intelligent lyrics are in both English and Spanish, but it's their eclectic range of styles and musical textures that keep them both fresh and difficult to categorize.