The Collaborative International Dictionary of English v.0.48:

gaga \gaga\ adj.
   1. mentally or physically infirm with age.

   Syn: doddering, senile.
        [WordNet 1.5]

   2. marked by foolish or unreasoning fondness; as, gaga over
      his girlfriend.

   Syn: crazy about, dotty, enamored, infatuated, in love,
        smitten, soft on(predicate), taken with(predicate).
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

gaga
    adj 1: mentally or physically infirm with age; "his mother was
           doddering and frail" [syn: doddering, doddery,
           gaga, senile]
    2: intensely enthusiastic about or preoccupied with; "crazy
       about cars and racing"; "he is potty about her" [syn:
       crazy, wild, dotty, gaga]

Moby Thesaurus II by Grady Ward, 1.0:

113 Moby Thesaurus words for "gaga":
   ape about, apish, asinine, balmy, bananas, barmy, bats, batty,
   beany, befooled, beguiled, besotted, bonkers, brainless,
   buffoonish, buggy, bughouse, bugs, bugs on, cockeyed, cracked on,
   crackers, crazy, crazy about, credulous, cuckoo, daffy, daft,
   dazed, dippy, dizzy, doting, dotty, dumb, empty-headed, fatuitous,
   fatuous, featherbrained, featherheaded, flaky, flipped, fluttery,
   fond, fool, foolheaded, foolish, freaked-out, frivolous,
   fruitcakey, fruity, fuddled, futile, gaga over, giddy,
   giddy-brained, giddy-headed, giddy-pated, giddy-witted, gone on,
   goofy, gulled, harebrain, harebrained, haywire, hepped up over,
   hipped on, hot about, idiotic, imbecile, inane, inept, infatuated,
   insane, just plain nuts, kooky, loony, loopy, mad, mad about,
   maudlin, moronic, nuts, nuts about, nuts on, nutty, off the hinges,
   off the track, off the wall, potty, rattlebrained, rattleheaded,
   rattlepated, round the bend, sappy, scatterbrained,
   scramblebrained, screwball, screwballs, screwy, senseless,
   sentimental, shatterbrained, silly, slaphappy, starry-eyed over,
   steamed up about, stupid, thoughtless, turned-on, wacky, wet,
   wild about, witless