Whenever I think of a non-synergistic character, Mundo comes immediately to mind. Let's give him a defensive steroid (scales with HP and resists) an AD steroid (scales with attack speed and crit) an AoE damage aura (scales with AP and MPen) and a percentage based skillshot (scales with MPen and CDR). The only options that really work are CDR tank and tanky DPS, and either of those really only takes advantage of a couple skills fully, just sorta using the others as filler.
On a side note, I was in a custom game with a friend who was trying Mundo for the first time (he rather liked having 170 AD at level 5 with only a Vamp Scepter) and he remarked "Man, give any other character any one of these abilities and they'd be ridiculous, but somehow when you combine them they actually get weaker."