(In alphabetical order according to their last name/nickname)
1) Roger Hodgson (Supertramp)
When he left Supertramp in 1983, then their popularity started to decline dramatically. After he left he followed a solo career the following years, with minor success, and then he released another album in 2000 after a long break. His biggest solo hit would be Had a Dream (Sleeping with the Enemy), reaching at #48 in Billboard Hot 100.
2) Billy Idol (Generation X)
Mostly famous as a solo artist, than with his work with Generation X. He had multiple Top 10 hits in many countries, especially during the 80s. Among all his works, the most interesting one would be Cyberpunk. Whilst it was a commercial failure, it was a unique and ambitious album (the way it was created), and way ahead of its time.
3) Mick Jagger (The Rolling Stones)
Despite his famous work with The Rolling Stones, he had a small, yet successful solo career during the 80s and 90s. His biggest solo hit would be Dancing In The Street, a duet with David Bowie which reached the #1 spot, in Australia, UK and Ireland.
4) Greg Lake (King Crimson)
He was the lead vocalist of King Crimson's best period (late 60s-early 70s), and later lead vocalist of Emerson, Lake & Palmer. As a solo artist he released two superb albums, with Gary Moore. His Self-Titled debut and Manoeuvres. Unfortunately they were commercial failures.
5) Annie Lennox (The Tourists)
Apart from the vocalist of The Tourists, a late 70s British New Wave band, she's mostly famous as the vocalist of Eurythmics. Her solo career is known as well, especially in the 90s. As a solo artist she followed a more Soul direction, than the Synth-Pop style of Eurythmics.
6) Limahl (Kajagoogoo)
Known mostly as the vocalist of Kajagoogoo's first album, featuring the big hit Too Shy. As a solo artist he's considered one-hit wonder, since he had only one, yet a big hit. Particularly Never Ending Story.
7) Nick Lowe (Brinsley Schwarz)
Another one artist that is considered one-hit wonder as well. His biggest hit was Cruel To Be Kind. What's more interesting about this song, is the fact that it reached #12 in five different countries. Particularly UK, USA, Canada, Australia and New Zealand. It might happen if a song reaches #1 spot, but it's a rare case for #12 songs. In UK he had a Top 10 hit called I Love The Sound Of Breaking Glass.
8. John Lydon (aka Johnny Rotten) (Sex Pistols)
And of course later with Public Image Ltd. There's not lots of stuff in his solo discography apart from his solo album Psycho's Path. Considering what it was going around in the 90s, it was a really good album, yet lacked success. Another known song of his is World Destruction, a collaboration with Afrika Bambaataa.
9) Phil Lynott (Thin Lizzy)
Also a founder of the short-lived band, Grand Slam. As a solo artist he released only two albums but very different than his Thin Lizzy works, leaning towards a more New Wave/Synth-Pop direction. His biggest solo hit was Yellow Pearl, which made it in the Top 20 in the UK and Ireland.
10) Eric Martin (Eric Martin Band)
Mostly known as the lead singer of the band Mr. Big in the 90s. His career before Mr. Big was unknown yet a very interesting one. With his original band, Eric Martin Band, he released a superb AOR cult classic called Sucker For A Pretty Face. As a solo artist he had a few albums, with I'm Only Fooling Myself being his best. All his works before Mr. Big were commercial failures though, unfortunately.
11) Freddie Mercury (Queen)
Obviously his work with Queen overshadowed his solo career, but still his solo work was pretty successful as well. The direction he followed in his solo-career was more closer to the sound of the sound Queen had during the mid-80s. His biggest solo hit would be Living On My Own (1993 version), which reached #1 in four countries.
12) Kim Mitchel (Max Webster)
Kim Mitchel followed a successful solo career during the 80s, especially in his homeland, Canada. Although his albums and singles had big success in Canada he didn't manage to make a huge impact in other countries neither as a solo artist nor with his band Max Webster.
13) Morrissey (The Smiths)
Well, to be honest I never liked him neither as a person nor as a musician. Still I feel surprised how he managed to be so successful, especially in the UK where he's adored both as a solo artist and with The Smiths (also overrated). He had multiple Top 10 hits, so I cannot define which was his biggest one.
14) Peter Murphy (Bauhaus)
Although not much famous in a mainstream way, he is famous among Post-Punk and Gothic Rock circles. In the early 90s he became somewhat Mainstream though since one of his songs, Cuts You Up, was a #1 hit in the US Modern Rock charts, and another one of his songs The Sweetest Drop, reached #2 in the same charts.
15) Stevie Nicks (Fleetwood Mac)
Despite her successful work with Fleetwood Mac, she had a successful career as well, with her solo debut Bella Donna, being her most successful, reaching #1 in the USA and in Australia. She's also famous for maintaining her youthful looks, of course. (Wow! Is this woman really approaching 70 in this photo?)
16) Chris Norman (Smokie)
Smokie is a Rock band that found commercial success in continental Europe. Not much in his homeland, UK. As a solo artist he had moderate success in continental Europe during the 80s. His most famous solo hit is Mignight Lady.
17) Gary Numan (Tubeway Army)
Even during his days with Tubeway Army, he was the one who was gaining the main attention so we could say he was a solo artist from the start. His biggest solo hit was Cars, and of course Are Friends Electric? with Tubeway Army. Since then his mainstream popularity declined, but he remains a cult icon till today.
18. Ric Ocasek (The Cars)
His solo works during the 80s had quite a big success, even though not as big as his works with The Cars. His biggest solo hit was Emotion In Motion, which made it in the US Top 20, but both Beatitude and This Side Of Paradise albums are superb.
19) Ozzy Osbourne (Black Sabbath)
The man had a series of successful albums since the beginning of the 80s. His biggest solo hit would be Crazy Train from his debut Blizzard Of Ozz. It made it in the Top 10 of six countries in total. His whole album Blizzard Of Ozz is a Hard Rock masterpiece though.
20) David Pack (Ambrosia)
Ambrosia was a Soft Rock band which had two big hits in late 70s and early 80s. How Much I Feel and Biggest Part Of Me particularly. Both reached #3. As a solo artist his most successful album would be Anywhere You Go, although success was minor.