Just for reference, ain't is in fact dialect, but many of the other examples you give aren't. It may help to look up the meaning of the word dialect in order to distinguish true dialect from differences in register, which seems to be partly what you're talking about. Especially in German, which has many true regional dialects that are much more distinctive than American regional accents, it's better not to confuse the issue.
Gonna and wanna, for instance, aren't special dialect words, they're just nonstandard spellings used to show colloquial pronunciation, like the examples Corinna gave of Hamse (Haben Sie) and Haste (Hast du). So that's really register, not dialect.
Martin Durrell has nice examples of register differences in his German reference book (Using German? I never can remember the title); he marks them R1 for colloquial/everyday (umgangssprachlich), R2 for standard, and R3 for formal, literary, bureaucratic, etc. (gehoben). Some of the differences have to do with grammar, like using 'wegen dem' or splitting up da-words like 'da nicht für.'
If you really want to read some true dialect, you could probably find books or plays with dialogue in well-known dialects like Berlin and Bavarian and Platt, and there have even been threads here in the forum with dialects like Swiss German (probably the hardest one) and Swabian.
Maybe people could suggest some other texts with a lot of colloquial German to read, either dialect or just everyday language. It does sort of help to see it written before you try to listen to it.
OT re Schubert: Fischer-Dieskau is always nice, and there are good budget-CD compilations, or used to be. (-: