Jet-powered boosters of convertional, vertical lifters.

[MedwedianPresident]

Back in .14 and .15, it was somewhat popular to use jet-powered boosters on normal, expendable vertical launch vehicles. They would be decoupled upon suffocation, at 20 to 25k. Do people still do this now?

The main advantage would be their reusability and higher efficiency as well as a longer burn time that varies with the steepness of the launch trajectory, the main disadvantage would be the rapid thrust falloff or asymmetrical burnouts that can lead to loss of control as well as the wasting of fuel.

[Blaarkies]

no, they are far too expensive and give too little thrust at takeoff for an adequate TWR. Old updates did not limit the maximum speed at which jet engines produce thrust, neither the maximum altitude so one could spam air intakes to make engines run at 5% thrust at 60km altitude.

Are you looking to save money with a simple design? Use the biggest parts that are practical for your lower stages(3.75m if you have to) and find how much you can supplement them with S1 kickback SRBs

Save more money? You will need to look at recovering the rocket then. 1 stage rocket that goes into stable orbit, deploys payload, returns to kerbin and lands in the vicinity of KSC (a single parachute and some propulsive landing is surprisingly easy to pull off)
This can lift payloads into orbit for the price of fuel, a fairing and maybe some kind off heatshield...but it takes longer per launch

[NSEP]

Jets are hard to throttle and only work for a brief time while going vertical. Its a no go for me. Not worth it.

[Foxster]

Very handy though for some challenges because of the excellent isp of jet engines. You can get to ~25km on a very small amount of fuel, keeping your craft mass low. 

[DAL59]

Use an expendable first stage, reusable second.  Make toroidal aerospike second stage, with airbrakes and rcs, and use 7 hammers for stage 1.  

[Mic_n]

If you're using something like the stagerecovery mod that lets you recoup (most of) the costs of the stage, so you're basically just paying for the fuel - then yes, they're still very useful, especially for lighter payloads like kerbin-orbital probes.  Does take a tiny bit of extra thought in using them - mainly in ensuring you manually shut them down and stage away before they flame-out.

 

The big benefit, as noted, is in the huge ISP they have - when you can get so much energy from so little mass, you can keep that exponential growth down.