ne haber - something like what's up, literally meaning "what is the news?" (informal)
haydi or hadi - come on
bilmiyorum - i don't know
gidelim - let's go
canım - my dear
güle güle - bye (for the one staying)
allahaısmarladık (we read it as alasmarladık) - bye (for the one in action/leaving)
görüşürüz (as Jennifer said) - Literally meaning we will meet (sometime), better to translate as "see you"
iyi akşamlar - good evening
iyi geceler - good night
günaydın - good morning
hoşgeldin or hoşgeldiniz - welcome
teşekkürler - thanks
teşekkür ederim - thank you
rica ederim - you're welcome (in return to thanks)
önemli değil - nothing important or not at all (in return to thanks)
Doğum günün (or gününüz) kutlu olsun. - Happy birthday (to you)
Nice yaşlar - Many happy returns
Bayramınız kutlu olsun - Have a merry/happy bayram
Yeni yılınız (or yılın) kutlu olsun or mutlu yıllar - Happy new year.
Take care of yourself - Kendine iyi bak
These are the ones i could think for now.
Görüşürüz :))
ps. kusura bakma(yın) - a kind of light apology asking not to see one's fault/culpa :)