I will exclude the three obvious choices of milky way, LMC, SMC and just go for the mostly telescopic/binocular ones - this is more the tourist "galaxy experiences" list
some of my reasons are nostalgic too
1, NGC 253 the "silver coin galaxy"
2, NGC 104 "sombrero"
3, M31 Andromeda galaxy and companion
4, NGC 5128 "hamburger galaxy"
5, NGC 1365 - i will never forget the first time I saw this galaxy properly thru an f5 13" at a dark site - blew us away! its so different to the rest
6, Leo triplet
7, NGC 55
8, NGC 4945 - smoky ghost of a galaxy - one of my first - sentimental
9, a drive thru the virgo cluster down thru to Coma Berenices with a large aperture @ low power at a dark site is something to behold - a river of galaxies!
10, NGC 7331 - nice little edge on - dont know why I like it so much? its just a nice snack after andromeda while in area
Kearn