A browser toolbar is a type of browser extension, and browser extensions serve to extend the functionality of (or override the capability of) web browsers, often based on users' common tasks. Although extensions are relatively new to Chrome and Safari (both began supporting them in 2010), they've been in IE since 1999.
People find extensions useful: whether this means being able to block annoying ads that follow them around on different websites, check Gmail without a separate tab, debug websites easily (many designers and developers use Firebug), see what a site looks like to users with disabilities (as with NoCoffee), or any of a slew of other purposes. Extensions serve as a tool to get people toward their end goals. The Chrome Web Store was formerly the Google Chrome Extensions Gallery, which shows that Google gave their support to the idea of extensions as well.
However, as the comments on your question have said, extensions have been thrown in to installers based on marketing decisions. These decisions die hard. For example, Alexa is still (as of 2014) considered one of the foremost ways to determine how popular a website is - even though it is still determined from which users are still using their toolbar. (Alexa itself says now that the ranks are determined by the users of over 25,000 browser extensions.)
If the Alexa toolbar were the only source of data for the rankings, wanting the rankings to remain an authoritative source would be at least partially an appeal to tradition. But "we've always done it this way" is a phrase commonly heard in software companies, particularly large companies. An example from my previous career as a developer: I asked a senior member of my team what he thought of his frequently 80-hour workweeks. He told me that the software industry just worked that way and every shop was like that. That had been his experience for decades working in similar large companies on similar projects. I read Death March while I was still working there and then got another job at a mid-sized company with a quite different culture!
At my last software development shop, I was one of the developers in charge of our flagship product's installation process with InstallShield. Although not a UX practitioner yet, I wanted to make various UX improvements like getting rid of the install process's repeating progress bars. I was told that that was just how InstallShield works. Our team was to focus on working on our company's product - only. And to some extent, that is a smart business decision. Seth Godin recently wrote,
"Steal, don't invent. ... When it comes down to the thing you will be
known for, your uniqueness, your gift, your thing worth talking
about--don't steal that. Writers shouldn't steal words from other
writers, and chemists have no need to steal the research of other
chemists. Sure, go ahead and invent.
"For the rest, honor those that came before and use their work as a
building block for yours."
The other piece of my answer deals with something Serhiy's comment touched on: tech laggards, those who say, "We've always done it this way", with respect to their tools. According to diffusion of innovations, late majority and laggard users display skepticism and lack of opinion leadership; laggards tend to be the oldest users, "in contact with only family and close friends". If you've experienced an older family member asking you for help getting rid of a browser toolbar on an old browser, you have interacted with a laggard.
One way to keep laggards from falling too far behind is automatic software updates, such as those pushed out by Google Chrome when the browser is restarted. But keep in mind: automatic updates only recently started to become more common. Many software upgrades are still manual, whether operating systems (e.g. Windows 8) or new releases of software. Upgrading could have a financial cost or just a time cost or interaction cost (e.g. having to type in a password to download an upgrade has kept me from upgrading on occasion!). People need to be sold on it, especially if they do the upgrade themselves. Otherwise, they'll look for ways to go back to the user experience that gave them what they wanted and a good state of flow (hence why we see articles on downgrading iOS).
So, if a laggard can't be sold on a software upgrade or a new tool, they stand to fall victim to the same vulnerabilities of the old tool - often without the safety net of the old tool's vendor (see end of support for Windows XP). These users, as Serhiy pointed out, are the prime target audience of malware (such as malware being embedded in toolbars). The malware developer holds a huge advantage over most of these laggards in terms of how well he or she understands the technology involved.
This brings me to another word in your question: "still". In the New York Times article I linked earlier in this answer, the laggard being interviewed was only 56 years old. Laggards are stereotyped as retirees who are going to die within the next few years. This was 10-15+ years ago. But laggards and late majority people are very much still around, even in workplaces. Some laggards haven't even retired yet. They have decades of life (and computer use) left, which in theory means that malware developers will have decades left to exploit them. I can think of one computer security presentation at one of my previous workplaces where they showed a screenshot of someone with around 15 browser toolbars on their screen, and I think it belonged to a co-worker down the hall who was having trouble with their computer. (This workplace required all of its employees to use only IE. I think IE was on version 8 or 9 at the time.)
And many of today's innovators and early adopters will become tomorrow's late majority and laggards. The diffusion of innovations theory has been around for over 50 years, and is still alive and well in each of its stages in our society.
Like Flash, until a major vendor (such as Apple) moves to stop supporting toolbars, many sites will probably be using them far past their usefulness. Even 3 years after Apple stopped supporting Flash, Flash is still very much alive on websites today.