I was wondering if counterpoint is still used today or was it something that was just used by Bach? Does modern music like pop songs use it?
Counterpoint is simply the relationship between multiple musical lines. As such, any excerpt of music with more than one line is displaying some sense of counterpoint, whether intentional or not.
Note also that there are multiple eras and traditions of counterpoint, each with their own distinct styles (what many erroneously call "rules"). Palestrina is typically considered the master of Renaissance counterpoint, with Bach being the master of Baroque counterpoint. Mozart and Beethoven were among the many masters of counterpoint in the Classical era, and getting into the Romantic era you have composers like Brahms and Bruckner. And in the twentieth century you have composers like Shostakovich and Hindemith, both of whom wrote sets of piano fugues much like Bach did.
If you're asking whether or not something like fugues are still written today, of course they are! In fact, the fugue at the end of Young Person's Guide to the Orchestra (1945) is still to this day one of the most impressive feats of counterpoint I know:
One practical use in pop, country, big band, (and probably jazz, maybe rock) is the counterpoint between melody and bass. One would like the melody and bass to be independent voices. Many bass players use chord inversions (playing the third usually) and walking basses to achieve this (and they do it on the fly.) If one isn't careful about parallels, the texture can suddenly seem "thin" like an instrument dropped out.
I like to think of songs as being a melody line (maybe several instruments), a bass line (using good two-part counterpoint), and a bunch of inner stuff that need not be so careful (because of doublings and texture, one doesn't usually hear multiple lines in these styles). Renaissance counterpoint sounds more like several independent voices but Baroque counterpoint (not counting fugues, canons, and inventions) can be a bass line supporting upper voices with some filler for chords.
I'd like to add an example. I'm suggesting that even popular music (since the Middle Ages anyway) has a skeleton consisting of a bass line and a melody line (or lines) with some chords thrown in between and a related but separate percussion part. Here's an example of a song with just a bass and melody exhibiting the point.
It is still used, but not the way Bach used it. Bach used to compose the different voices to be harmonically interdependent but rhythmically independent. After a certain point (later 19th-early 20th century) the composers took counterpoint in a different direction. They started composing for voices that were purely independent with each other; both harmonically and rhythmically.
A great example is Arnold Schoenberg and his use of 12-tone serialism.
Here is a more modern piece that uses contrapuntal techniques:
Also, here is an example from Radiohead's In a glass house:
Notice how the horns move independently from the voice and the rhythm section and how the clarinet moves in a different rhythm that the brass.
I get the feeling the question is more along the lines of: is there counterpoint in homophonic music, or is a homophonic bass part a contrapuntal line?
I think the answer is yes to both.
It's very common in pop/rock for the bass to move only by leaps to roots while the vocal melody moves in a more step-wise manner. By necessity those two lines are independent in terms of contour and relative motion. And, in pop/rock it would be very common for the bass and voice to be rhythmically independent.
Independent contours, independent rhythms: how is that not counterpoint?
The discussion on this post... Is there any name for two melodies that are being played at the same time? ...still sticks in my mind as making a muddle out of a simple idea: independence of contour and rhythm makes counterpoint.
Well, Scarborough Fair by Simon&Garfunkel qualifies as pop music I think and works with contrapuntal themes, even if they are slightly disentangled to accommodate reception.