Pastebin offers itself as a gratis paste service. Although it is probably the most well known option out there, it is certainly not the best.
The security issue
Pastebin has a couple of issues that harm the visitor's security. This on itself should be considered such a bad practice that no-one should consider their service at all.
Cloudflare is a MITM. It completely breaks the secure chain of TLS on the web, and should not be used. Any service still using Cloudflare should be shunned. There is another article on this site which has more information on this specific issue. In addition, Cloudflare can be considered a privacy issue for the same reasons, as is detailed below.
Another issue with regards to security on pastebin are the advertisements. While it can be argued that "they need to make money somehow", using ads always seems like the worst possible solution. Especially given the way they're serving it. The past couple years have shown that advertisements on the web are easily abused to serve malware to good netizens who decided to not block all ads.
A rant on the state of ads might be appropriate, but this article is specifically about Pastebin, so I will just keep it at "third party advertisements are a security risk, avoid sites who use them"
The privacy issue
Apart from their security issues, Pastebin also offers some privacy issues. As stated above, they make use of Cloudflare. This means that whenever you visit them, Cloudflare takes note of this. They may even decide that you need to perform some additional tasks in order to be allowed to the resource. This doesn't happen to most users, but if you're using any anonymization practices, this will happen almost every time you visit a site behind Cloudflare.
In addition to telling Cloudflare, you will also tell another third party, Google, in case this "additional step" is required. This is done via the new reCaptcha system which will inform Google of almost every detail of your browser and the behaviour used to solve the puzzle. Incredibly useful for fingerprinting you accross multiple locations.
Then there is Tor
But, if you're using an anonymization proxy such as Tor, even if you do not care about the Cloudflare issue, and you solve the "security check" presented to you, Pastebin still refuses to offer you their service. If they are going to refuse you service, they should tell you up front, not after you have already informed two other harmful parties of your attempt of accessing the resource.
Actually, they should not. They should simply not require you to give up your privacy and serve you the content you were looking for. Blocking resources to a certain group of users is simply censorship, and should not be the status quo on the free internet.
Luckily, there are plenty of alternatives that do not treat their users with such disrespect. I ask anyone who is still using Pastebin to stop doing this, and use any of the alternatives.