I would suggest never giving login details to your account to anyone.
Facebook, Twitter, Google Analytics, Webmaster Tools, many bigger hosting companies and probably other sites allow you to add people to your account.
Facebook Pages and Twitter accounts can have multiple admins with different levels of control.
Hosting companies have similar and the added bonus of added admins not being able to see/control payment info.
If you give login details it is possible for the person to change your “Recovery Email” etc and so they could make things very difficult for you. If you are unsure how to do it, simply search “add someone to my (website name) account” and follow the instructions.
Also, anyone who offers services like this should know about these methods and not ask for your login details. Personally, I would be suspicious of any who do ask for those details if a safe alternative is available.
Some of the Content Management Systems/Website builders do not have this option so be careful when choosing one to use.