As a German learner I also wonder about this. Some that I have come across so far are:
'kriegen' (to get) used in the same way as 'bekommen'
eg. 'where do I get something to drink?' 'wo kriege ich etwas zu trinken' (or more colloquial spoken "wo krieg' ich 'was zu trink'n" (obviously this is only how it would be spoken, not written))
'hinkriegen' manage or wangle
eg. 'I barely managed to pass the test' 'ich habe kaum hingekriegt, den Test zu bestehen' ("ich hab' kaum hing'kriegt, den Test zu b'steh'n)
'kapieren' to get, catch on, twig, understand
eg. 'I didn't get the joke' 'ich habe den Witz nicht kapiert' ("ich hab' den Witz nich' kapi'rt)
'(an)gucken' to look (at), watch, see
eg. 'I am currently watching a film' 'ich gucke gerade einen Film (an)' ("ich guck' g'rade 'nen Film (an)")
As I said, I'm a German learner, not a native, so apologies for any grammatical or other errors, especially with my interpretation of the elisions and contractions for colloquially spoken German (as I understand it unstressed vowels (such as many 'e's) are almost omitted entirely in spoken speech, which I've tried to represent with all the apostrophes).