Having the right tools to do a job is an incredibly important factor for both the success of that job and the success of the employee / volunteer / worker. Sadly, not all organisations provide the correct tools (sometimes no tools at all) which has bad implications. While I'm largely thinking about tools for my industry (computer, peripherals, company mobile phone) this concept applies in all industries.
There are absolutely companies out there that provide their staff all the right equipment. Sadly, in my experience, this is the exception rather than the rule. It's also important to remember the tools have to be of good quality - it's worthless issuing equipment that fails after six weeks.
The human factor
I'm going to start with the human factor, as well being / mental health / psychology is increasingly mentioned in my work place. By giving someone the right tools, be that computer equipment, books, screwdrivers, vacuum cleaners, or whatever, the organisation is saying "we value you and your contributions". There's something special about being allocated something that's for your use, even more so when that equipment isn't a hand-me-down from your predecessor.
Don't underestimate the morale boost from giving an employee or team member dedicated, appropriate, equipment.
"There's no budget"
This seems to come up everywhere I've worked. I'm not naive, I know money can be tight. Equally I know money can be found when it's needed, it's all a case of prioritisation.
When I worked at the school it was convention that the headmaster had the best laptop - think high end Sony Vaio. There was always budget for that, and he went through laptops at a rate of roughly one a year. Some were stolen (left on the back seat of a car), others were dropped or otherwise manhandled to breaking point. Let's put this in perspective: a lot of what the headmaster did was work in Microsoft Office. While important work, it didn't warrant the £900+ laptop he was destroying so readily. Eventually I bit the bullet and just issued the same £300 Acer that the regular teachers got. Every cost my department incurred was calculated in our own unit of currency known as "percentage of laptop" and the headmaster didn't need 300% of a laptop every year.
If there are any managers or employers among my readership, I'd implore you to think carefully before playing the "no budget" card, especially if it's known among the staff that the managing director just got a new Jaguar company car, bought outright in (company) cash. Again this comes down to morale and telling your employees that you value them.
"Only small organisations don't provide equipment"
Sometimes I've been met with shock when friends, or worse clients, have realised that it's not only the small organisations that expect their staff to provide their own kit (more on that in a moment). I've worked for employers of various sizes, in various sectors. One employer had around 250 staff (I'm guessing, but it sounds right with an ICT department of around 41 people. There was clearly some budget around, yet our engineers were seemingly expected to provide their own screwdrivers .
For context, I've had to provide my own equipment (or supplement it) in more employments than I've been provided what I need. When you consider that the smallest organisation I work for, APF (I write eVitabu for them), very quickly purchased an Android tablet for me to develop on it's clear that the smaller organisations aren't always the ones not providing the equipment. It's worth noting APF have offered to reimburse me the software subscriptions that I have paid for that I need to develop for them (PHPStorm for one, and Trello as some of its paid for features would be helpful). I've turned that offer down, as I use those applications for personal projects too, but the offer was almost mind-blowing when I consider what their turnover is compared to my employers over the years.
Using your own tools
Undoubtedly, many of us have ended up using our our tools to get a job done. In the past I've provided my own screwdrivers for fixing computers and provided my own laptop. While this may be convenient (it gets the job done), it's not without risk.
I recall in one job I wasn't supposed to be a field engineer, but I'd regularly be sent to one client as their Windows NT4 network was not to everyone's liking (or skill set). In theory there was always a pool laptop I could take to a customer site, while in practice it was never available - either already in use or broken. This led to me taking my Dell Inspiron Mini 10 (in bright red) to customer sites. It was a nice little unit (if you ignored the trackpad, which was awful) that, for its time, did an admirable job of most tasks I threw at it. The laptop ran Windows XP, dual booting Linux, so I was covered for most tasks.
It would be accurate to say that one customer was surprised I was having to provide my own equipment. They were equally surprised to find that particular employer didn't provide sick pay (!). We both acknowledged the risk I was taking in the event the laptop was damaged while at a customer site, or stolen from the company van .
That's the thing: by using your own equipment you are taking a significant risk that you'll end up without that equipment. One accident (a cup of coffee knocked over the laptop) or one "forgetful" colleague that borrows your screwdriver and again forgets to return it means you'll be out of pocket and the organisation a) probably won't care and b) won't be reimbursing you.
Security risks of your computers
It would be remiss of me, given my role, not to mention this. Your organisation probably (hopefully!) has a set of security controls in place on its own laptops - mandated anti-virus, requirement for legitimate software etc. By using your own laptop you introduce a risk to the organisation and potentially its clients. If it was found that your equipment caused a cyber security incident it's not going to end well for you (expect "you shouldn't have done that" long before "we should have given you a laptop").
Conversely, consider the security risk to your equipment. Not every system you connect to will be friendly, so why risk your equipment or data?
Capable, versus preferred, tools
This is an important distinction, and one I feel it's worth highlighting. In some cases I've provided my own equipment because I preferred it to what I was issued by the organisation. For example, I provide my own pens and ink because I prefer a fountain pen over a scratchy, cheap, office ballpoint pen. I also brought in my own mouse because it was nicer than the stock mouse provided in the box with a PC.
Both the mouse I was given, and the office ballpoint pen, were capable tools - they would perform the task asked of them. I just didn't like them, so I swapped them out. If I choose to swap out a tool (and I'm allowed to) then I accept the risk of using my own equipment. Someone could borrow my desk and spill coffee on my mouse but I wouldn't try to bill the company (I'd be miffed if there wasn't an apology note though!). I don't expect an organisation to provide me the precise tool I want because it's my preference, although if there's a legitimate business case then I'd expect there to be some discussion.
Wouldn't it be good though if every employee got to choose their own mouse, keyboard and screens?!
This probably comes across a bit angry, and I don't see that as an entirely bad thing. Too many employers expect their employees to make up for the organisation not providing adequate equipment, and that needs fixing. A quick Google search shows I'm not the only one saying staff should be given the right tools.
So, if you're a business owner, manager, director, team leader, share holder or someone who has influence, please make sure your teams are given what they need.
 One of the managers was even joking that their team had to provide their own tools, apparently missing how wrong that idea was.
 Said employer did provide a van, but did not provide satellite navigation. These were the days where Tom Tom had a good market share and Google Maps wasn't readily usable on smart phones. I ended up providing my own sat nav too.