I read that the sentence, "The Tigers are my favorite team," is grammaticaly correct. I've always thought the proper verb was "is". Does anyone know the rule?

We generally go with grammar by form for such matters in the good ole US&A. "The Tigers are …" vs. "Detroit is …" For teams with singular names you would see, e.g., "Cornell is …" and "Big Red is …" In the UK you will frequently see grammar by meaning with such constructions as "Arsenal are …"

But it's grammatically correct to say the "the lemon and banana ARE on the table." I don't understand why "team" shouldn't always take the verb 'is'.

Tigers has an s.

When reading British periodicals, one comes across the following sort of constructions:

"The Ministry are letting contracts ..."
"The Ministry are preparing for ..."

These sounds off to the ears of residents of the USA because we think of a department of government as being a unit, an entity, a single thing and single things take singular verbs. To reach the mindset of Brits, it is necessary to mentally add some words, e.g.:

"(Officials of) the Ministry are letting contracts ..."
"(Members of) the Ministry are preparing for ..."

the real answers is: teams (a collective treated as singular noun) should use is.
HOWEVER- some collective nouns are treated as plurals, this is especailly true, (but not exclusively true) if they end in an S.
Finally--there is no way to know which collective nouns are exceptions--they generally are local idioms. (Local being used to define a variety of english, (UK, US, etc))

Dam'd if i can think of an example right now, but others will join in with more examples--hundreds...
and while most will be american (US) english idioms, not all will be. One has already been provided- (Arsenal)

When you're listening late at night
You may think the band are not quite right
But they are, they just play it like that.

[Geo. Harrison. Only a Northern Song]

they just play it like that. Rimshot

Thank you.

As far as I'm concerned, it's "the Tigers is," but it just sounds funny, and people can't be bothered.

Quote:

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As far as I'm concerned, it's "the Tigers is," but it just sounds funny, and people can't be bothered.

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If it sounds funny, apply Safire's Rule:

If it sounds funny, the hell with it.