Autism Speaks is probably the most notorious and the most prominent Autism "charity". It has a lot of celebrity endorsements, but does that make them a good organization to support? Not necessarily.
For one thing, Autism Speaks uses fearful, hateful and dehumanizing rhetoric to try and get people to donate to their organization. They've compared being diagnosed with Autism to being struck by lightning, being diagnosed with cancer and AIDS among other things. They believe that a person is better off dead than being Autistic. Perhaps their most infamous PSA is I Am Autism in which they say that Autism breaks up marriages, causes embarrassment and shame to families and prevents your child from making friends - all of which is most certainly not true.
Plus, Autism Speaks has very little actual Autistic representation in their leadership positions. Only 2 out of 31 people on their Board of Directors are Autistic, while 12 of those 31 members are from major corporations, such as Viacom, CBS, SIRIUS Satellite Radio, etc. If you're going to have an Autism organization, the vast majority of your board members have to be Autistic. It's as simple as that - and they have to be from more diverse backgrounds, with different races, genders, sexualities, etc.
Only about 4% of Autism Speaks' funds goes to their "Family Service" grants, which is designed to help Autistic people and their families. In 2014, Autism Speaks' budget comprised of 35% of research funds (and most of that research was for prevention and cures for Autism, not actually helping Autistic people.), while 33% of that money went to media, "awareness" campaigns and lobbying, 23% of those funds came from fundraising, 5% went to management, while an abysmal 4% went to "Family Services".
If you really want to support Autistic people, here are some better alternatives:
Autistic Self Advocacy Network - run entirely by and for Autistics, ASAN does advocacy and policy work to ensure that Autistic people can life their life to the fullest.
Autism Women's Network - aims to help Autistic women and girls. It is trans and nonbinary-inclusive, too.
Self Advocates Becoming Empowered (SABE) - empowers self-advocates with disabilities, as the website implies.
And if there's any other helpful organizations/charities I missed, let me know in the comments.
Boycott Autism Speaks
Before You Donate to Autism Speaks, Consider the Facts (PDF)
Nothing About Us Without Us!