Just an idea, I haven't tried this, but SoundHound 1) supposedly recognizes tunes from singing the melody. 1) http://www.soundhound.com
music.stackexchange.com/users/7251/Matthew James Briggs
Non-expert opinion:
Are you widely distributing it?
Is it possibly from a piece of music that still may be under copyright (link) ?
You could pay for a search or the advice of an entertainment attorney.
Otherwise, you might like to know just for your own understanding, but it probably isn't worth the effort, aside from maybe asking some experts.
If you have an artist in mind, you could listen to their collected recordings.
If it's only a few chords in the progression and you don't recognize it, it's probably not very identifiable.
music.stackexchange.com/users/17048/dwn
You can do that only for recordings, not tunes.
For tunes you should officially register the tune to your name and claim your rights if by chance you notice someone other is using that.
This can happen if the tune goes popular.
If it doesn't go popular, then claiming and searching is also impractical.
Visit copright.gov and My Free Copyright for more information on registering tunes (and also recordings).
You can also use your local official time stamp agencies or notary for the same purpose.
For tracking recordings, I can suggest these services: Tunesat scans the tv stations and websites all around the globe and gives a periodical report of usage of your recordings.
This is a relatively expensive service for amateur uses.
Rumblefish scans YouTube and claim royalties but can be accessed only through agents like CDBaby , Tunecore ...
etc.
music.stackexchange.com/users/17019/Guney Ozsan
Yes, there are no exact way to find out if a tune is exist ant now, simply because there are too many songs and most of them contain a lot of notes.
However, there are cases where small parts of your song matches other small parts of other songs.
To answer your question, if your song is a piano song you made, try searching it up in the piano melody search engine, called http://www.musipedia.org/ .
This website lets you input a song or melody into its search engine, and searches it depending on if you want rhythm or melody to be searched more.
Keep in mind, it only works on piano songs as this website only contains these songs.
This website is great to see if your song matches or is close to another melody, as it will sort it from most likely match to least likely!
I use it to check for common tunes and if my songs are close to others.
Enjoy!
music.stackexchange.com/users/17168/kmart
I know of no way to do it, but YouTube is inordinately successful at recognising copyrighted video even when it's been re-captured on a mobile phone, etc.
So I'm quite sure that technologically it would be possible - but it would need someone like Google to build it.
music.stackexchange.com/users/15313/Mr. Boy
For copyright questions, one thing you could consider doing is searching for the tune on Peachnote.com to see if it exists in that database of 200,000 out of copyright musical sources (mostly classical).
If it appears in there then you don't have to worry about whether it appears in an in copyright song because you'd be protected since it'd be derivative of a melody that has already passed into the public domain.
music.stackexchange.com/users/5807/Michael Scott Cuthbert
When I come up with a lick/melody, there always lingers that question of "Has this melody already been used?" Should I worry about it or is there a way to find out without too much hassle?
Any quick way to know if my tune is already used?
music.stackexchange.com
<melody>
music.stackexchange.com/questions/27342
music.stackexchange.com/users/13617/manejar
It is rather difficult to find out if a tune you have come up with has been used before. One option may be to try SoundHound http://www.soundhound.com which is supposed to recognize tunes when you sing the melody. If you have an artist in mind, you could listen to their collected recordings. For copyright questions, one thing you could consider doing is searching for the tune on  Peachnote.com  to see if it exists in that database of 200,000 out of copyright musical sources (mostly classical). Some people would doubt whether it's possible to find this out since there are so many songs in existence. However, there are tools out there that might recognise music that you play, such as SoundHound, musipedia or Peachnote. Alternatively, if you have an artist in mind, you could simply listen to their recordings to see if you recognise something that you have composed.
If you have an artist in mind, you could listen to their recordings to see if you can identify your composition. Some people would doubt that there is a way of doing this because there are simply too many songs to consider. There are a range of tools out there that might be able to recognise music that you play, such as SoundHound, musipedia or Peachnote.