'Our team are playing really well today'
That sentence is absolutely standard in British English, but unusual, 'ungrammatical' even, to American ears. The word team denotes a group of people, and is usually referred to as a collective noun. The standard position amongst grammarians and usage guide writers is that you can use either a singular or plural verb with a collective noun.
There is a difference, however, between American and British usage. While Americans will practically always use a singular verb, British speakers will often use a plural verb, something some people find hard to accept.
During the course of a (let's say lively) discussion on this topic on a language forum, I collected quite a lot of quotes from, and links to, various grammar books, style guides and commentators on English, so I thought it might be useful to gather them all here.
In no sense am I trying to persuade people to use plural verbs with collective nouns: that is your choice. My aim here is just to try and convince people that this usage has a long history and is entirely legitimate.