A quick at-a-glance guide to my opinions on the pavilions:
Definitely worthwhilePavilion of Future. If you love plants and botany, don't miss it. Line, but no tickets.
Expo Dome. This is the place where you can see the entries of flower and gardening competitions. Line, but no tickets.
Pavilion of Regimen. Amazing bonsai displays. Tickets needed.
Expo Hall. Quality stage shows. Check listings. Long wait to get in; no tickets.
Taipei Story House. Historic house with interesting collection of period furnishings. Don't miss the 1935 promo film. Tickets needed.
Go if you have the time or inclinationPavilion of Dreams. Maximum weirdness, but crazy waiting/ticketing system. Tickets needed.
Theatre of Dreams. An adjunct to the Pavilion of Dreams. Animated short video by Jimmy Liao, supplemented with some animatronic effects. Line to get in.
Expo Theatre. Short 3D animated movie about landslide. Poorly fitting 3D glasses provided. Tickets needed.
Pavilion of Culture. Small, but interesting displays on aspects of Chinese culture. No line or tickets.
Palace of Flora Teas. Lovely stroll through Taiwanese gardens and traditional old home. No tickets, no lines.
Taipei Fine Arts Museum. Regular modern art museum. Free entry if on Expo grounds. Gauguin exhibition extra. No lines or tickets.
Pavilion of Aroma of Flowers. Nothing more than a souvenir shop. Go if you want a souvenir. No lines or tickets.
Don't waste your timeEcoARK/Pavilion of Fashion. Boring building made of plastic bottles. (Go only if you like fashion shows and can time your entry to see one). Line to get in.
Pavilion of Angel Life. Silly art display followed by sillier animated short. So, are they rabbits or cats?

Line to get in.
Celebrity's House. Unless you're a fan of Teresa Teng, don't bother. Even if you are, you may be disappointed. Tickets needed.