What are some TV shows similiar to Doctor Who?There is nothing quite like Doctor Who, in its scope, variety, longevity, and quirkiness, but depending on which aspect of the show appeals, I can make various recommendations.
If you want a long-running science fiction epic then the combined weight of the various Star Trek series will probably do. You could also try series like (the new) Battlestar Galactica, Stargate and its various spin-offs, Babylon Five and Farscape, but you will find they lack the variety of Doctor Who, each one revolving around the same set of characters in the same situation (more or less).
If you want something with the same kind of British fantasy charm then probably adaptations of late nineteenth or early twentieth century children's fiction are your best bet. Think of works by E Nesbit, Lewis Carroll, P L Travers, C S Lewis. At a pinch, J K Rowling, but not J R R Tolkien whose work has a rather different flavour.
If it's specifically British telefantasy that you want, especially if it's the "classic era" of Doctor Who which appeals, then you should certainly try Sapphire and Steel, The Avengers, The Prisoner and Blake's Seven. If your tolerance for camp is a bit higher, then you could also try Department S, Adam Adamant, The Persuaders and Jason King.
If it's the humour of the show which appeals, then you could try The Hitchhikers Guide to the Galaxy, especially if you've seen and liked the Tom Baker story City of Death. If it's specifically Russell T Davies' writing, then his recent series Cucumber was excellent as was his landmark series Queer as Folk (these aren't family tea-time viewing though). If it's specifically Steven Moffat's writing which you're after, then try his series Coupling, Joking Apart and Press Gang.
If it's the anthology nature of the show which you like, then check out the original run of The Twilight Zone.
But there's nothing else quite like Doctor Who.