I have a 13-inch MacBook Pro with the default resolution 1280x800. I would like to know if there exists the possibility of having a better resolution?
Sorry, no. The resolution of the display panel itself is only 1280x800, so there is no way to display more without physically replacing the panel.
There is an app named Retina Display Menu. You can find it like rdm.tar on google and it allows you to switch to whatever resolution you want on your Mac. I have a MBP mid 2012 running 1440x900 as native and it works perfectly.
Retina Display Menu actually works perfectly, and is exacty what you're looking for.
I personaly like to play poker, and by adjusting up the resolution I can have multiple games going on at my 13" screen without any trouble, beforehand the desktop size was to small to allow multiple games
Whilst not quite for the same reason, I have displayed a higher resolution on my Macbook that it is physically capable of producing natively, by screen sharing from my macbook onto my iMac. I've found that any increase in screen real estate is massively negated by the poorer quality of the display, which is by necessity reduced in detail in order to maintain the appropriate size. Not worth it, in my opinion.
What you can do, in an attempt to also "fake" the overscan method that bmike mentions, is to enable screen sharing on your local macbook, and then using a seperate VNC client, connect to yourself (i.e. localhost, or 127.0.0.1), and configure the VNC client to provide a larger overscanned/panned/scrolling display, but this is also a fudge, and can be proper irritating, especially when you consider the fixed dock and menubar that may both be hidden at any one time.
You can just plug in a 21" flatscreen to act as a 2nd screen using a DVI adapter. Then change the resolution of the new screen (via dock settings) to 1600 x 1400 (or similar), then you have a 13" display plus a 21" display. The 21" display isn't just a scaled up 13" picture either. You can see whole documents that you would need to scroll through on the 13" screen. I've dragged large documents across from one screen to the other: on the laptop screen you only see half the document at any one time, on the 2nd screen you see all of it plus margins!
You can do it virtually using SwitchResX, but it looks really bad. I changed back within a few minutes.
you can do it as a "devoloper". No need for a developer account though. download Xcode from the Mac app store. this video will show u how
Yes, you should try this http://specialmeaning.blogspot.com/2016/07/yes-apple-i-did-it.html
Install Xcode from AppStore and follow the guide to setup maximal resolution.
The program output for MacBook 2016 for example:
Current resolution was 1440x900 Supported resolution modes: 640x480 800x600 1024x768 1280x800 1440x900 2048x1280 1152x720 2304x1440 2560x1600 is the selected top one.