Extensive use of hiragana by intent will make yourself look immature, childish, unserious, drowsy, cute, innocent, or sometimes less intelligent, depending on the context.
A good but exaggerated example is found here. A very childish character in a game, who is always talking in hiragana.
…ふわぁ…あなただぁれぇー?…ぷろでゅーさー?…えぇー…かわいいー?…あいどる?うんー…いいよー…やるぅー…あいどるやるぅー。…で、なにするのー?…わらうのー?…ふわぁ
Huuuoaaa... who are you? a produucer? eeeh, ... cuuute? an idool? yup... ookay... i do... i do, idol ... so what do i do...? to smile...? Huuoaa....
Combination of 長音符(ー) and hiragana, which is generally prohibited, is also a good way to add extra childishness, as in "とーきょー" instead of "とうきょう" (東京 or Tokyo).
In addition, recently, extensive use of smaller hiragana, when possible, has a similar effect. It has become a popular way of chatting via their smartphones among young schoolgirls (google 若者言葉 or ギャル語 for details and more extreme examples).
See the following example (the last one may be rather extreme):
今日は雨が降っているよ。 (It's raining today.)
=> きょうは、あめがふっているよ。
=> きょーは、あめがふっているよ。
=> きょーゎ、ぁめがふってぃるょ。