From what I've encountered in spoken and written German so far, I can see two (and a half) cases:
Literal meaning
"auf jeden Fall" can mean literally "in any case" or "always".
Auf jeden Fall musst du nach links und rechts schauen, bevor du über die Straße gehst.
meaning
In any case you have to look left and right before crossing the street.
Filler word
"auf jeden Fall" and "jedenfalls" are sometimes used to start a sentence as a filling word. This is mostly used in spoken, but not in written language (see a list of fillers):
Jedenfalls bin ich dann früher nach Hause.
Auf jeden Fall bin ich dann früher nach Hause.
meaning
Anyhow, I went home early.
"Auf jeden Fall" can be used literally and as filling word, "jedenfalls" only as latter.
Modal particle
The word "jedenfalls" can shift the focus a bit, often restricting a statement in the sense of "at least"
Ich war (jedenfalls) pünktlich zuhause.
I, at least, was home on time. [But I can't speak for others.]
or
Das hast du (jedenfalls) früher immer gemacht.
(At least,) you used to do that. [But maybe/apparently not anymore.]
or
So scheint es jedenfalls.
Or so it seems.
Edit: In response to the comment that only suggested I'm wrong without specifiying exactly how, I'm adding a few sources and a third case I neglected.
http://synonyme.woxikon.de/synonyme/jedenfalls.php lists many words as synonyms for "jedenfalls" that have completely different meanings.
http://de.wiktionary.org/wiki/jedenfalls states two meanings:
1: an Vorangegangenes anknüpfend: auf alle Fälle, bestimmt
2: an Vorangegangenes anknüpfend: nach, trotz dem, was vorher geschehen ist
which I'd translate to
1: following something previous: in all cases, surely
2: following something previous: after, despite what happened before
See the following example sentence from http://de.thefreedictionary.com/jedenfalls
Ich weiß nicht warum, aber jedenfalls hat sie ihn verlassen.
I don't know why, but she left him.
To me, this sentence doesn't change its meaning if you omit "jedenfalls":
Ich weiß nicht warum, aber sie hat ihn verlassen.
This site lists many fillers and "jedenfalls" is even part of a list of fillers to avoid
Instead of downvoting and telling me I'm wrong, it would probably be more helpful for the author of the question if you tell me how I'm wrong or provide a better answer.
