Large and rugged; sturdy or chunky — coarse/rough in appearance or feel (colloquial). 'ごっつい' is more emphatic.
彼はごつい手をしているので、器用そうには見えないが力は強い。
He has big, rough hands; he may not look dexterous but he's strong.
ごっついブーツを履いて山道を歩いた。
I walked the mountain trail wearing chunky boots.
あの機械はごつくて頼りになる。
That machine is rugged and reliable.
Unrefined; boorish — describing someone or something lacking refinement or polish (colloquial).
彼の話し方はごつくて、初対面では好印象ではなかった。
His manner of speaking was rough, and it didn't make a good impression at first meeting.
その店員はごつい態度で客に失礼だった。
That clerk was rude to customers with a coarse attitude.
Extreme; excessive — used to emphasize something that's over the top; colloquially intensified as 'ごっつい'.
今日は風がごっつい強くて外に出られない。
The wind is terribly strong today; I can't go outside.
その値段はごつい高いから、ちょっと手が出ない。
That price is ridiculously high, so I can't afford it.