Many hosts these days offer a domainname included in the package, while many registrars also have hosting packages for a small extra fee.

I wonder if it is wise to purchase a hosting package with my registrar or not.

The advantage is that if you experienced your registrar's support is fast and reliable, you are sure to have the same level of support for your site.
Disadvantage: if anything goes wrong, both your site and your domain are in troubles, whereas otherwise only site or domain is in danger.

What do you think? Is it better to keep hosting and domains seperated, or not?

My opinion is keep them seperate and do each well while cross-promoting the heck out of both.

The problem with some registrars today is they want to offer everything under the sun, and they do none of it well.

Keep them very seperate, I have heard many horror stories(I am sure you have too)

well there is no 100% correct answer for this option since both options might be good and might be bad.

it all depends on the hosing company and the registrar.

look it from the other way around, your hosting company is perfect and your registrar is bad and something wrong happens to your domain you'll blame them and vica versa.

the big thing is just making sure you can transfer the name away in the event something ugly happens with your registrar

I would say NO. A domain name now costs only a few dollars, and it's not worth the risk at all. I have quite some *free* domain registration credits laying there untouched.

I think the bigger challenge is when they include a free domain name with hosting and you need to end the hosting early. It would be hard to move away at that point