I like Rings of Saturn a lot ! (they are core-y too as well) I absolutely love Gojira.A lot of passion from these french guys.
On the melodic side , well I like Nekrogoblikon , their instruments are like [insert honey analogy here].I like Kalmah , an awesome band with super melodic sound.Finally I also like Whispered , quiet a unique of a band .. melodic death with japanese instruments like koto and stuff.
edit : oh i forgot to mention I also like Thrash. Lich King would be the best example here.I also like punk but they have to be like The Exploited...
edit2: on the slam/brutal death I like Abominable Putridity
I will most definitely check them out.One good thing you get from talking to metalheads is music suggestion