Well, it would help if you get the Japanese subtitles with it (only available with the Japanese Region 2 DVDs unfortunately).
If you like Totoro, check out other Studio Ghibli works, such as:
Kiki's Delivery Service (̑} [܂̂イт])
Porco Rosso (g̓ [EȂ̂Ԃ])
Nausicaa of the Valley of the Wind (̒J̃iEVJ [̂ɂ̂Ȃ])
Laputa, Castle in the Sky (V̏郉s^ [ĂÊ냉s^])
Grave of the Fireflies (ΐ̕ [̂͂])
and a whole other bunch of shows. Lol.
Here you can find more information on the shows. Most Studio Ghibli animes are family oriented, though some are more violent. If you're not the type to watch really depressing shows, stay AWAY from Grave of the Fireflies. Man that show is so sad... As for another good family anime to watch, try Kiki's Delivery Service, it's very good. Think along the lines of Spirited Away, though I seemed to enjoy Kiki's Delivery Service more. Personal tastes, I suppose.