Does this exist? A Concert alert service.
 

Do you know what would be great? If I could give a website a list of my favourite artists, and it would send me an email whenever one of them was performing in a show within 300km of my city.

Is there anything out there that does this? I'd pay for a service like this. I can't keep track of all the listings at all of my local venues, and I keep missing artists that I like.

LastFM sort of does this, but not particularly well. If you enter your city, it will provide a list of upcoming shows.

Ents24 Tickets - Live gigs, comedy, theatre, shows and days out across the UK

For the U.K at least. Decent site with detailed listings.

JamBase has a show alert email service. Might be what you're looking for.

Concert Tickets, Reviews, Concert Tours and Live Music Shows. Go See Live Music > JamBase

I agree with you, but also it provide concerts from cities near you (near meaning not always quite near). At least that's what it happened in my case.

Last.fm's concert listings do the trick for me...

Check out Songkick

Does exactly what you're asking for... Can scan through your iTunes or any music library (or just enter your own favourite bands) and will instantly alert you if they are playing nearby with links to tickets

TheList - (jrl version)

the list has been a saving grace for years