Of the following two phrases advise me as to the correct one. "I
graduated college last year". OR  "I graduated from college last
year".

"I graduated from college last year".

In the preferred meaning, it is the college that does the graduating;
the graduate is on the receiving end.  Therefore, the hypercorrect
expression is:"I was graduated from college last year."  
http://dictionary.reference.com/search?q=graduate

Alanna, I want to bear your children. I know it doesn't work that way,
but you're worth it!

You are the first person in over 20 years I have heard provide the
correct usage. The last time was in 1985 in a James Kilpatrick article
on language.

Mark wants to bear Alanna's children?

Yes, quite!  I suspect that Alanna learned English as a second
language, and that this fine destinction is made in her mother tongue,
perhaps German (although not always observed these days:  "Er wurde
promoviert.").

Hmm, some interesting propostitions here. Is there a grammar gene? 
English is my first language. (I'm a lexicographer's daughter, if that
means anything)

Alanna,
A lexicographer's* daughter?!  Well, that's almost as bad as having
been raised speaking German.  ;)  But I am sure you are a very nice
person and don't volunteer finer points of grammar unasked.

*  "A writer of dictionaries; a harmless drudge, that busies himself in tracing 
    the original and determining the significance of words."
        142.206.72.66/2002/08/s0701_e.htm   (who's that?)

    I am sure he isn't, much more likely following in the footsteps of "the
    great lexicographer".

Regards, Myoarin

If my question had focused on graduation from high school, I have a
hunch that probonopublico's answer would have been correct.Right?

Please take it from me (an Englishman) that, in every day usage, "I
graduated from college last year" is perfectly correct.

Changing 'college' to 'high school' matters not.

All the Best

Bryan

Bryan, I agree  - as an American who went to a school and a college
where Alanna's "hypercorrect" usage would not have been found quaint -
 but it was unusual.

Like Mark, I was very pleased with her pointing out the better usage.

Cheers, Myo