There has been that annoying Sprint commercial (https://www.youtube.com/watch?v=xRibRj770J8) on the TV lately where Malcolm McDowell screams out "Totes my goats!". So I've googled that but was not satisfied with the explanation from the urban dictionary and sites alike. So what is it anyway?
Totes is a shortened form of totally, amplified with the common present-day slang suffix -s (compare, for instance, awks for awkward). It was documented on Urban Dictionary as early as 2003 and has probably been around considerably longer: totally itself was identified by F.Zappa and M.U.Zappa, (“Valley Girl”, 1982) as a core emphatic in Proto-Valspeak.
Totes magotes is an emphatic reduplicative form, comparable to easy-peasy or itty-bitty. Several sources attribute its first appearance, and perhaps its coinage, to the 2009 bromantic comedy I Love You, Man (but, again, it may have been around longer)†:
SYDNEY: You know what, we should jam together sometime, man.
PETER: Yeah! Totally! Totes magotes! Cool!
A comment on this very clip at YouTube clearly (and possibly ironically) demonstrates exactly the same formation processes at work on “crazily adorable”:
Totes McGotes, it's cray-cray adorbs. —TheAndrewj96
The suggestion by Damkerng T. and the source linked by fayalif, that the gotes piece represents G.O.A.T. = Greatest Of All Time is attractive and plausible. I suspect, however, that this is a retrospective folk etymology. Certainly most users betray no consciousness of this origin, spelling the syllable gote rather than goat.
† And now Eric Duft's answer establishes that the phrase was in use as early as 2001.
I haven't ever seen the movie I Love You Man. I had several friends that used the term back in 2001 and 2002. The same friends would use the term "cool beans" and "cool beans marines". The term "totes magotes" in synonym form means awesome or slang "sweet" or right on, or cool bro, right on man. For an example, person #1 says "I think I gotta drop some anchor man"; person #2 says "right on bro, have a good time." Foreign example: person #1 says "I think I gotta drop some anchor man"; person #2 says "totes magotes, have a good time."
While I cannot authoritatively prove it, I think it is a nonsense phrase that is just meant to convey emotion in a meaningless way. Compare "Yahoo!" (the word, not the site) which derives from a degenerate species of humans in Gullivers' Travels but means excitement, and "All my eye and Betty Martin." which conveys an opinion that it's trash.