Modish public speaking coaches will tell you that it’s OK to say "uh" or "um" once in a while, but the prevailing wisdom is that you should avoid such "disfluencies" or "discourse particles" entirely. It’s thought that they repel listeners and make speakers appear unprepared, unconfident, stupid, or anxious (or all of these together). Perhaps the biggest foe of "uh" and "um" is Toastmasters International, which charges speakers a nickel for every "filled" pause (that is, for every pause that’s not silent). Each of their 12,500 clubs around the world has an official "ah" counter.
But "uh" and "um" don’t deserve eradication; there’s no good reason to uproot them. People have been pausing and filling their pauses with a neutral vowel (or sometimes with an actual word) for as long as we’ve had language, which is about 100,000 years. If listeners are so naturally repelled by "uhs" and "ums," you’d think those sounds would have been eliminated long before now. The opposite is true: Filled pauses appear in all of the world’s languages, and the anti-ummers have no way to explain, if they’re so ugly, what "euh" in French, or "äh" and "ähm" in German, or "eto" and "ano" in Japanese are doing in human language at all.