Actually, most of the new artists, with lack of creativity, steal "old" songs.
And this is the truth!!!
Being a huge fan of 60's to 90's songs, and I know most of them, I noticed a lot of old songs back on radio, and they actually have success.
But... they are all remixed and weird songs are added.
So I must say, I hate today's music, I don't see skills anymore, only an overdose of synthetiser.

My favourite music group is actually Saga, which were one of the first to use the synthetiser, and they are really great at it.

And I must say: Old songs still have influence, because they are still on the radio!!!

Funny! xD
Just sayin' there's no more instrumental skills, like guitar, drums and stuff... only synthetiser.
It's not every group, but most of them. (Yay for Linkin Park)

Rap is mostly a poem with a beat.
There's no great solo or anything, just a repetitive beat.
But it is considered music, for some reasons (Eminem.)

Let's come back on topic now.
Most of the song's lyrics today are talking about sexuality.
BUT, sometimes, They steal lyrics from old songs.

They do have influence because:
1. This "old" music is popular on radio, because today's artists, in lack of creativity, steal music from older artists. (If you want a proof, watch Dirty Dancing (Old movie from the 80's)
2. They also steal lyrics.
3. There is still millions of "old" music fans around the world. It can be Classic, Heavy Metal, Prog Rock, Pop, etc.

Going on influences from the past some are even in the mainstay, or popped up in some music. If any of y'all listen to Ke$ha Iggy Pop from The Stooges and so on was featured in the song Dirty Love off her new album Warrior.