Does anyone else have a problem getting inspired to finish a song?

One of my problems is I start a song but then can't find the inspiration to finish it. Here are two examples of songs I recently made, that I probably won't finish...

Anyway, my basic question is, how can I overcome this? How can I get inspired to finish my compositions?

Nah, I never have that problem. Sometimes I need to give a melody a little while for me to think of a creative way to use it, but I'm always quite eager to work on my music until it's finished. Hell, many of my compositions were processes that spanned two years.

Very often I'll write the ending very early on, so I know where I'm headed. It makes writing the middle easier.

I have a similar problem sometimes. Usually it occurs when I'm at a block, so I start move away from the work, part consciously part not. It's pretty common with the beginnings and ends of my pieces, those are the toughest parts for me to compose. I'd just suggest looking at motivic/thematic material you've produced already, and alter or add something new to it to wrap up your piece.

Yeah, I get that block sometimes as well. The sad thing is there is no definite and scientifically proven way to get you inspired. It just suddenly hits you. I'd agree with most of the people here that you can try looking at your themes/motifs and making some variations, a sketch maybe here and there, and see what you can come up with. Sometimes you'll end up with something pretty interesting in return.

You can also try searching for more stimuli. It could be a fantastic meal in an exotic restaurant, a place you've never been to, a good movie or whatever. You might get something in there that has some relevance to your present material. Who knows, such experiences might hit you with that sudden creative energy everybody's craving for.

You need to think about a piece COMPLETELY in a lot of senses of the word before you write it in a "finished" way.

If I have any issues finishing a piece, I find it really helpful to take a break from it for a couple of weeks without thinking about it or practising it. When I go back to it, I try to get an idea of where I want it to go (similar to a story; with a beginning, middle and end).
As a backup plan, if this doesn't work, I'll sometimes just improvise in the same key as the piece to look for new ideas...!

I had this problem many times... I always write tabs for anything I come up with, so as to start making a song out of it... but then I get discouraged and find whatever I did boring, too conventional or too similar to something I already did, and I leave it there. So now I have a lot of tabs, which I listen to again to get ideas (after some time I get the feeling i didn't wrote them).

Listen to music to write music.