If you only had 4 different yeasts...

I would have US 05, wlp 099, 530, and 028.

WLP 028 and 530 for beers and braggots
WLP 720 for meads and melomels
EC1118 for misc wines

Alright, we'll go with:

Wyeast 1469 West Yorkshire Ale
Wyeast 3787 Trappist High Gravity
Wyeast 3724 Belgian Saison
Wyeast 1728 Scottish Ale.

The first two are my house strains for many of my beers, English and Belgian respectively.

The other two, well, I love Saisons, and that's my go-to. The 1728 is versatile enough that not only can I brew Irish and Scottish ales with it, but American styles too, depending on the fermentation temperature. I can also us it to dry out beers that the 1469 can't do (strong English ales).

I enjoy German beers, but not as much as the English and Belgian ones.

I'd go with 1469, roselaire blend (never made a sour, but what the hell), maybe cal lager (2112) and 3711. I could make pretty much anything I wanted with those, I think.

wlp007
WY1450
WY2124
Wy3787

WLP 029 (ales)
WLP 860 (lagers)
WLP 720 (meads & ciders)
Lalvin R2 (wines)

conan
1098
3724

& some bugs

Fun thread. How about:

Wyeast 1968
Wyeast 1450
Wyeast 3711
WLP 029

Us05/001
Roeselare
W 34/79 -
Wlp550

Wlp007
Wlp530
Wlp001
Wyeast 2124

WLP090
WLP029
WY1272
S-04

I don't really do lagers so I don't have any favorite lager yeasts.

Easy since I rarely use anything other than Cali ale, chimay, south german lager and dennys favorite.

WLP833 Bock Lager
WY3068 Weihenstephan
US-05/WY1056/WLP001
WY1469 West Yorkshire

Denny's Favorite
Scottish Ale
Nottingham
US-05

WLP 007
CONAN
Wyeast 1728
WLP 410

my four desert island yeasts would be WLP005 (Ringwood), WLP001, WLP530 (Westmalle), and lucky dip