Human SNP databases other than dbSNP
I'm pretty sure there are no public databases of variants that aren't included in dbSNP. That is the variant database so that's the one you want to use. 

While there are various other databases around, they tend to use dbSNP rsIDs as well so any variants in those will also be in dbSNP. So while dbSNP is nowhere near complete, of course, it's still the most complete one you're likely to find.