Imposter Syndrome
Essentially, it's the opposite of the Dunning-Kruger effect. You feel that your skills are less than those of your peers and that you're just skating by on luck. One day, someone is going to discover you don't really know what's going on and bam, your career is over. Is this an irrational fear for most of us that have it? Of course. Does that change the fact that we still feel incompetent when rating ourselves against our peers? Nope!
So, how do you get over it?
That, my friends, is the real question. Some days I'm able to overcome it just by looking at the work I've done. Other days, I need to look at my "feathers" file. If you don't have one of these, you should start. Essentially, take any positive feedback you get from anyone you work with and put it in a folder (file, email, evernote, dropbox, or an actual physical folder). It's the "I'm having a shitty day and need to be reminded that I'm a good person" folder. Whenever you're having an "off" day, take 10 minutes and look through it randomly. This folder also helps when it comes time for your self-review or if you're looking for a raise.
Other days, not even that will help. On those days, you just soldier on, try not to push any code that'll break production or the build, do any yak-shaving that needs to be done. Basically, you want to try to prevent reinforcement of the imposter syndrome.
The final way that I deal with it is work on a side project. Usually it's work related, something that's very niche, something that just makes me happy. Obviously, this isn't always an option so sometimes I just push through the day and when I get home I work on something like that. Woodworking, chainmaille, whatever it is, it's usually something not computer related.
To paraphrase Tim Ewald in Programming With Hand Tools
The more I spend time with computers, the more I need to spend time with things that aren't computers!
And that, for me, helps me to realize that computers aren't the sum total of my existence. My code is not me.