英文结尾
There are some slight differences in connotations of each letter ending. I'll order them in increasing formality.

Love
Very personal. Used between lovers, family and close friends.

Cheers
Very casual. Used between friends. Can be used between coworkers if you want to appear very casual, at the risk of sounding unprofessional.

Take care
Casual and used between friends.

Thanks or Thank You
'Thanks' is very casual and 'Thank You' is formal. Usually used in a business setting. 'Thank You' is a great way to end an email to a stranger, especially if you are making a request or asking a question.

Yours or Yours Truly or Truly
Casual or Business casual. A more personal, but still polite way to end the letter. You've probably met the recipient in real life.

Best or Best Wishes
Casual or Business casual. A polite way to end the letter. Can be used between friends or strangers.

Sincerely or Sincerely Yours or Yours Sincerely
Casual, Business casual or Formal. The standard letter ending. 'Sincerely' is the most versatile ending because it can be used to end either casual or formal correspondence. If y
ou're unsure about how to sign your letter, use 'Sincerely'.

Regards or Best Regards
Business casual or formal. You would use this if the recipient is someone you haven't met in real life.

Cordially
Formal. Used in business correspondence when the topic of the letter is serious. Sometimes used if there is a conflict between the sender and the recipient.

Using an ending that is too casual for the situation may not always be inappropriate. Conversely, using a casual ending can show your self-confidence. But to do this requires you to gauge whether the recipient would like a more casual conversation.
Love
个人性质。用于爱人，家庭或者亲密的友人。


Cheers
随和性质。用于朋友。如果你希望看起来平和一点，也可以用于同事，但有不太正式，显得不专业的风险。

Take care
随和，也是用于朋友的。

Thanks or Thank You
Thanks偏随和，而Thank You偏正式，常用于商务场合。当你给陌生人写信，尤其是请求协助，提出要求或者询问事项时，Thank You是收尾的好选择。

Yours or Yours Truly or Truly
日常交往或者商务场合都可以用，虽然有一点点随意，但还是一种礼貌的方式。一般用于你之前见过面的对象。

Best or Best Wishes
日常交往或者商务场合都可以用，是一种礼貌的方式。对朋友和陌生人都可以用。

Sincerely or Sincerely Yours or Yours Sincerely
日常交往，商务往来或者正式文书都可以使用，是标准的结尾方式。Sincerely是最为通用的形式，无论日常和正式通信都可以使用。如果不确定怎么结尾署名，就用sincerely吧。

Regards or Best Regards
商务往来或者正式文书。如果你和收信人没有在现实中打过交道，就用这个。

Cordially
正式。在商务谈判场合，当信件话题很严肃的时候使用。有时，当你和收件人之间有分歧或者冲突的时候，可以使用。

在正式场合使用一个随和的结尾并不一定意味着什么不恰当的事情。有的时候，这样做可以
显得你很自信，谈话很随和。然而，这样做之前请了解一下对方是不是喜欢这种随和的方式。
除了几位答主提到的语气不同，还有诸位都没提到一点，英文比较正式信或者是商业信件中yours fathfully 和yours sincerly跟开头称呼是有固定搭配的。
参看BBC的Learning English
括号里的是简略翻译
Beginning and ending the letter
We can now begin the letter but leave as much space as possible so that the body of the letter sits tidily in the middle part of the page.
（信正文部分放在纸的中间）
If you know the person you are writing to very well or are on friendly terms, begin simply with the first name, Dear Mary or Dear Henry.
（如果跟这个人很熟或者友好，用Dear+first name）
If you don't know the person you are writing to so well, but know of him as a named individual, start with title and surname: Dear Mr Potter or Dear Dr Baker 英文信件结尾or Dear Miss Taylor or Dear Mrs Cook or Dear Ms Barber. If you are not sure which of the last three titles is appropriate in any particular case, it is probably best to stick to Ms.
（如果不认识这个人，只知这人名字，用Dear+title(Mr/Dr/Miss/Mrs/Ms，不知道女性婚否，就用Ms）
Finish this type of letter with Yours sincerely. It is not necessary to insert a comma after beginnings or endings. If you know the person you are writing to well, it may be appropriate to insert a closing formula, such as With very best wishes, before the ending itself.
（结尾用Yours sincerely，前后不用加逗号。如果你跟你写信的那个人很熟，直接加With very best wishes结尾）
Sign the letter with your first name, if you are on first-name terms, or with your full name, if i
t needs to be a little more formal, but without any title. Your full typewritten name and designation (on separate lines) should appear beneath your handwritten signature.
(如果给人去信开头是那人first name，你也first name落款，稍微郑重一点，就不加title全名落款。上面是手写签名，清晰打印签名放手写的下面。)

If you do not know the name of the person you are writing to, begin with Dear Sir or Dear Sir or Madam or Dear Madam and end your letter with Yours faithfully, followed by your full name and designation.
（如果你不知道你去信的人的名字，开头用Dear Sir或者Dear Sir or Madam或者Dear Madam，结尾用Yours Faithfully,然后落款）
同时可参考Using Yours faithfully and Yours sincerely.
‘Yours faithfully’ or ‘Yours sincerely’ in a business letter?