Fetching details from the dictionary...

to adhere to; to stick to; to cling to
to keep close to; to go along with
to get involved with; to be thick with; to become intimate
シールがくっついて剥がれなくなった。
The sticker stuck and won't come off.
猫がくっついて離れないので可愛かった。
The cat stuck close and wouldn't leave, so it was cute.
ガムが靴の裏にくっついてなかなか取れなかった。
Gum stuck to the bottom of my shoe and wouldn't come off easily.