Since this lively thread carries on, I thought I'd add in my two cents' worth (or, rather, that of both The American Heritage Dictionary and The Concise Oxford Dictionary).

What I've always loved about the AHD are the synonyms and usage notes which are invaluable with word confusions such as this. And they don't disappoint now. Here's what they say, verbatim, for both 'obligate' and 'oblige':

ob-li-gate | transitive verb | To bind, compel, or constrain by a legal or moral tie. See Synonyms at force. See Usage note at oblige.
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o-blige | transitive verb |
(1) To cause to do or refrain from doing something; constrain by physical, legal, social, or moral means.
(2) To make indebted or grateful. Used with 'to' .
(3) To gratify the wishes of; do a service or favor for.
oblige | intransitive verb | To do a service or favor; perform a courtesy.

"Usage note: In the sense of rendering a service or kindness, oblige, favor, and accommodate are frequently interchangeable. Oblige and the somewhat more forceful favor generally apply to gratuitous service. Accommodate can be used in that sense, but is applicable also to business dealings, such as to services provided by banks, hospitals, hotels, and the like. Oblige and obligate are interchangeable in the sense of genuine constraint, but not in instances involving a sense of gratitude for a service or favor. A person is obliged (not obligated) when he feels a debt of gratitude and nothing more; he is obligated (or obliged) when under direct compulsion to follow a given course."
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And while I'm not going to type out the entire entry under 'force' here are the most applicable parts:

"Synonyms: force, compel, coerce, constrain, necessitate, oblige, obligate. These verbs mean to make a person or thing follow a prescribed or dictated course ... Oblige is applicable when compliance is caused by the operation of authority, necessity, or moral or ethical considerations, and obligate when compulsion is exerted by terms of a legal contract or promise, or by the dictates of one's conscience or sense of propriety."

As for The Concise Oxford Dictionary, here we go:

Obligate v.t. Bind (person, legally or morally) to do.
Oblige
(1) v.t. (arch. or Law). Bind (person, oneself) by oath, promise, contract, etc., to person or to do.
(2) Be binding on; constrain, compel, to do; make indebted by conferring favour, gratify by doing or with, perform a service for (person requesting it, or abs.).
(3) v.i. (colloq.) Make contribution to entertainment (with song etc., or abs.).

And "much obliged" is simply defined as "thank you"
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Personally? I got much more from AHD, as usual. Hope y'all find it useful too.