The only dice I am really comfortable using are the Platonic solids, which are dice of the 4, 6, 8, 12 and 20 sided variety.
I have great difficulty warming to the D10, as it’s not a regular shape, I always feel that a D10 is a die less likely to be fair. I’m sure that this is an unfair assumption to make, and I’m aware that D10s can very easily be used to roll a percentage value, which is often very useful, but I will always tend to avoid such rolls where possible, unless extremely fine grained results are required, a D20 will provide your percentages in 5% increments, which is often perfectly adequate.
As for specialist dice, such as a thirty sided die, I am deeply unsure that there could ever be a real justification for using one, where one of the standard dice type would be truly unsuitable. If there is a reason other than ‘coolness factor’, then I’d love to hear it.