Faith Hill opened for Tim McGraw during his 1996 Spontaneous Combustion tour. He proposed right before a performance one night, and they married shortly after the tour ended. They're arguably country music's most famous couple currently alive.
The second most famous country couple currently living would be Garth Brooks and Trisha Yearwood, who toured together in the '90s while Garth was still married to Sandy Mahl, and got married a few years after Garth and Sandy got divorced.
As for country music's most famous couple ever, Johnny Cash and June Carter Cash (among other infidelities, their affair ended his marriage to Vivian Liberto). The Carter Family performed with Cash for a few years and, in 1968, during a live performance in Ontario, Cash proposed to her. They remained married till her death in May 2003, four months before Cash himself died.
In an unfortunate example, bassist Nikki Sixx of Mötley Crüe slept with the only female member the band ever had, touring drummer Samantha Maloney, and almost broke up his marriage with Baywatch star Donna D'Errico because of it (they did eventually divorce several years later).
Lacey Moseley of Flyleaf and Joshua Sturm of Kairos
Most of the members of the band Eisley (who, btw, are all siblings or cousins to one another) married partners in the music biz. Vocalist Stacy Dupree married Darren King, drummer for Mutemath; guitarist Sherri Dupree married Max Bemis, frontman of Say Anything and is the ex-wife of Chad Gilbert of New Found Glory; drummer Weston is married to Jessie Munns of Luvbeat; and guitarist Chauntelle Dupree was formerly engaged to Adam Lazzara of Taking Back Sunday and ended up marrying guitar maker Todd D'Augustino. Bassist Garron Dupree is the only member not married to someone in the industry (yet).
David Vincent of Morbid Angel married Gen, frontwoman for Genitorturers.
Karen Fairchild and Jimi Westbrook of Little Big Town married in 2006 but didn't tell their two bandmates until two months later.
Imagine Dragons opened for Nico Vega at a 2010 concert in Las Vegas. The two bands' respective lead singers — Dan Reynolds and Aja Volkman — fell in love and eventually married. They also formed another band, Egyptian, as a side project.
David Vanian, frontman of The Damned, married Patricia Morrison, bassist of Sisters of Mercy, and they have a daughter.
Duane Peters, singer of punk band US Bombs and also a pro skateboarder, was married to and had a child with Corey Parks, former bassist of the psychobilly "sleaze rock" band Nashville Pussy.
Chris Brown and Rihanna, were close friends before they started dating years before it was officially announced to the press in 2008. Most people know how the relationship ended. For those who don't, let's just say it wasn't good.
They've never stated otherwise, but it's generally accepted that Beyoncé and JayZ first started dating when Jay-Z asked her to be on his song "'03 Bonnie and Clyde". They've been married ever since, and have become the most (in)famous couple in urban music.
Lachy and Emma of The Wiggles (the current Purple and Yellow wiggles respectively) have been dating offscreen for about 2 years. They got engaged as of recent too and married(update: they divorced in 2018). Even the children knew something was going on.
Morgan Rose, the drummer of Sevendust, was married to Rayna Foss, bassist of Coal Chamber. They have a child together as well.
Guitar god Steve Vai married Pia Maiocco, bassist of the all-girl hair metal band Vixen.
Nick Lachey met his wife Vanessa when she played his love interest in his video for "What's Left of Me", which is ironically about his divorce from his first wife Jessica Simpson.
Jamie Bell and Evan Rachel Wood met when they played a couple in the music video of Green Day song "Wake Me Up When September Ends". They got married seven years later and had a son, but separated in 2014.
Shakira met her husband footballer Gerard Piqué while filming the music video for "Waka Waka", the official song of the 2010 FIFA World Cup.
No Doubt: Frontwoman Gwen Stefani dated bassist Tony Kanal in the '90s. Their breakup was the inspiration behind No Doubt's biggest hit "Don't Speak".
Gary Barlow of Take That met his wife Dawn when she was hired as a dancer for the final tour before the band broke up in 1996.
In March 2019, Mel B Of The Spice Girls said that she had an affair with Geri Halliwell during the band's heyday.
Australian band Lo-Tel had their breakthrough hit in 2000 with Teenager of the Year, when it featured in the film version of Looking for Alibrandi. The film's star, Pia Miranda, featured in the music video and soon married Lo-Tel frontman Luke Hanigan. As of 2019 (when Miranda won Australian Survivor) they're still married with two kids.