Molina was born in Paddington, London. His mother, Giovanna (née Bonelli), was an Italian house-keeper who cleaned rooms in a hotel and worked as a cook. His father, Esteban Molina, was a Spanish immigrant from Madrid who worked as a waiter and chauffeur. Molina grew up in a working class district in Notting Hill that was inhabited by many other immigrant families. He decided to become an actor after seeing Spartacus at the age of nine, and attended the Guildhall School of Music and Drama.
In 1978, Molina starred with Leonard Rossiter in the sitcom The Losers. Molina made his film debut with a minor, but memorable role in the 1981 film Raiders of the Lost Ark as Indiana Jones' ill-fated guide, Satipo, during its iconic opening sequence. However, his big break came with Letter to Brezhnev in 1985, which he followed up with a starring role in Prick Up Your Ears in 1987, playing Joe Orton's lover (and eventual murderer) Kenneth Halliwell. He was originally cast as Arnold Rimmer in the TV sitcom Red Dwarf, but he was replaced by Chris Barrie.
Molina was a ubiquitous presence on British television in the early 1990s, with his most high-profile role being the lead in the first two series of El C.I.D. Subsequent film roles included Species, Dudley Do-Right, Chocolat, Not Without My Daughter and Enchanted April. With a mid-western American accent, Molina starred alongside Betty White in the US television series Ladies Man, which ran from 1999–2001.
He has worked twice with Paul Thomas Anderson, first in Boogie Nights and then Magnolia. In 2002, Molina gained wide recognition for his portrayal of Diego Rivera alongside Salma Hayek in the biopic Frida, a role which garnered him BAFTA and SAG award nominations. In 2003, he played himself alongside Steve Coogan in Coffee and Cigarettes. In 2004, Molina gained further commercial recognition when he was cast as the villain Doctor Octopus in Spider-Man 2, which went on to become one of the highest-grossing films of that year. He later reprised his role of Doctor Octopus in the video game adaption of Spider-Man 2 and archive footage of Molina as Doctor Octopus is seen in the opening of Spider-Man 3. In 2006, Molina portrayed Touchstone in Kenneth Branagh's film version of Shakespeare's As You Like It and appeared in Ron Howard's adaptation of The Da Vinci Code. Molina provided the voice of the villain Ares in the 2009 animated film Wonder Woman.
Molina's stage work has included two major Royal National Theatre productions, Tennessee Williams' The Night of the Iguana (as Shannon) and David Mamet's Speed-the-Plow (as Fox). In his Broadway debut, Molina performed in Yasmina Reza's Tony Award-winning play Art, for which he received a Tony nomination in 1998. In 2004, Molina returned to the stage, starring as Tevye in the Broadway production of Fiddler on the Roof. For his performance he once again received a Tony Award nomination, this time for Best Actor in a Musical. Molina received his third Tony Award nomination for Red in 2010, for Best Performance by a Leading Actor in a Play.
In 2007, Molina narrated a 17-part original audiobook for Audible.com called The Chopin Manuscript. This serialized novel was written by a team of 15 best-selling thriller writers, including Jeffery Deaver, Lee Child, Joseph Finder and Lisa Scottoline. The novel won the 2008 Audiobook Of The Year Award form Audio Publishers Association.
On 1 April 2010, he opened at Broadway's John Golden Theatre in the role of artist Mark Rothko in John Logan's drama Red opposite Eddie Redmayne for a limited engagement through 27 June. He had played the role to much critical success at the Donmar Warehouse in London in December 2009.
In 2010 he starred opposite Dawn French in the six-part BBC sitcom Roger & Val Have Just Got In, with a second series in 2012.
He is the only actor to have three Lego Minifigures modelled after him, with them being Doctor Octopus from Spider-Man 2, Satipo from Raiders of the Lost Ark and Sheik Amar from Prince of Persia]].
In July 2010, it was announced that Molina had joined the cast of Law & Order: LA as Deputy District Attorney Morales. He previously guest-starred in a two-part crossover in 2005 in two other Law & Order franchise shows, Law & Order: Special Victims Unit and Law & Order: Trial by Jury.
Molina is a patron of the performing arts group Theatretrain. Molina is also a longtime member of the Los Angeles theatre company The New American Theatre, formerly known as Circus Theatricals, where he often teaches Shakespeare and Scene Study along with the company's artistic director Jack Stehlin.
Molina resides in Los Angeles, California, and announced in 2004 that he had become a U.S. citizen. He is fluent in English, Italian and Spanish.
He married actress Jill Gascoine in 1986 in Tower Hamlets, London. He has a daughter, London based photographer Rachel Molina (born 1980), from a previous relationship, and two stepsons (Adam and Sean), from Gascoine's first marriage. He is also a grandfather to Alfie (born November 2003) and Layla (born May 2006).
In addition to acting, Molina is an Acquired Immune Deficiency Syndrome (AIDS) advocate. Not only does he donate towards AIDS research, but also participates in the Los Angeles AIDS Walk and recently played a role in Joseph Kibler's (a 21 year-old AIDS survivor's) documentary Walk On.
Molina is good friends with actor John Lithgow.