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One of the tactics I have been using with my clients for many years is something I call internet service separation.
This is where I use different providers for different aspects of the internet service that the client needs. 
This doesn't go down well with many internet companies (whether this is Internet service providers, web hosts etc). They like to have control over everything, get you to use their service for everything etc.
This isn't for your benefit despite what they may say in their sales brochures. It is for their benefit as it makes it much more difficult to leave them. You have to juggle all of the services being disconnected at the same time. For many people, especially those who don't understand how the internet works, they will not want the hassle. It is that reluctance to move that allows companies to get away with poor service.
You should have different companies for the following tasks:

• Domain Registration.
  Use a specialist such as 123-reg.co.uk here in the UK, or Go Daddy or register.com in the US. Don't use them for anything else (despite what they might tempt you with).
  Use a big provider, which limits the chances of them going down. Although most of the domain name registrars are actually using the services of one of the others, so in the event of a failure you may be able to rescue the domain name. 
• Internet connection.
  This should come from a service provider who gives you the best deal. Unless you are on a managed service, use your own kit. Routers etc, so that you have control.
  The only thing they should be giving you is IP addresses. Everything else should come from other suppliers
• Web Hosting.
  This should be with a dedicated host. The web hosting market is so competitive that the choice is endless.
  Try to steer clear from free web hosts - the old adage of "get what you pay for".
  However you don't have to pay over the odds for hosting - especially if the site is a simple static brochure type site. 
• Email.
  Ideally you should be using your own email server. I am an Exchange specialist and this posting is from an Exchange server point of view. 
  Although, if you have more than five or six staff, you are getting to the point where you can justify your own server. This doesn't have to be Exchange - there are many low end options that will provide you with in-house email services without the complexity of Exchange.  

Your Domain Name
The thing that internet service companies all want is to get control of domain name. Preferably transferred to their own domain name registrar, or in to the master account at their pet domain name registrar if they aren't one already.
As that is your company identity, you don't want to loose it. Once they have control over the domain name, they can effectively hold you to ransom.
Resisting attempts to gain control over your domain name is very difficult, and trying to get hosting companies to comply with something else can be a challenge. They can do it - they just don't want to - as there is nothing in it for them.
I have even had companies say that they cannot do what I need them to do - which is a outright lie. Very shortly afterwards they will usually lose the business. For one UK ISP this meant a loss of over £20k in annual revenue as I took a large number of home user accounts, a leased line and other services away as well - I actually had an account manager on the phone begging to be given another chance and crying when they found out.

Despite what any web hosting company, ISP or whoever states - you do NOT have to transfer your domain name to them to use their service.

A domain name transfer is just a way of getting control and also earning themselves some more money from the transfer fee. 
All you need to do is ask them for their name servers, ask them to put your domain name in to their name servers, then enter the name servers in to the relevant option at the domain name registrar.
You have maintain complete control. In the event that you want to move your web site to another host, then you just need to change the name servers. The hosting company doesn't need to know anything about it. I have changed hosts many times, and the first the old company knows about it is when I ask to terminate their service. At that point I am not using them for anything, so if they cut me off immediately, it doesn't impact my web sites in any way.
If you do change the name servers, then you need to use the web hosting company to manage your DNS. Make sure that you have the correct entries in place first.

A better option is not even use their name servers.

Ask for the IP address of the web site and enter that in to your DNS at your domain name registrar. This is often a good idea when you are hosting your own email, as it is not uncommon for web hosts or ISPs to "reset" their DNS records which set the MX records back to their email servers rather than yours.
Protect the domain name like you would any other asset of the company. Make sure that you do whatever it takes to ensure that it remains under your control at all times.