Game Programming Careers?

Writing your own games as a hobby, is generally much more rewarding than working on "My Little Pony's awesome cuddly wuddly family fun game", so to some extent that makes every programming job in the industry tedious to some extent. YMMV. Occasionally you'll be engulfed in a moment of complete and total awesome, but for the most part it's hard graft. If you're allergic to hard work, it might not be the career for you. In addition to the ones you've listed, off the top of my head....

Tools programmer (Maya/Max plugins, custom C# apps, MySQL asset management, etc)

Core Tech Programmer (low level maths, rendering, & engine code. maintain the core libraries)
Field Application Engineers (technical support role, typically a job role found in middleware or hardware vendors)
Analytics Engineer (interfacing the game with some form of analytics middleware to keep track of how the users play your game)
Build Engineer (maintaining the build server, deciding when to merge feature branches, etc).

R&D (doing interesting maths stuff, preparing patent applications, filling out claims for R&D tax credits)
Gameplay engineer (puts together bits of gameplay in script and/or C++)
GUI programmer (write the code to handle the GUI elements)
QA Engineer (Helps to develop the test harnesses)
Team lead / Product Owner (The boss of a development team)

which are the least tedious when it comes to coding?

This depends ENTIRELY on you.

Some people love writing graphics code. That is their dream. Other people find it tedious or even hate it.

Some people love writing networking code. That is their dream. Other people find it tedious or even hate it.

Some people love writing tools. That is their dream. Other people find it tedious or even hate it.

Some people love writing game scripts. That is their dream. Other people find it tedious or even hate it.

Some people love writing database code. That is their dream. Other people find it tedious or even hate it.

Some people love working with sick animals. That is their dream. Other people find it tedious or even hate it.

Some people love being at sea and working on boats. That is their dream. Other people find it tedious or even hate it.

Some people love cutting and styling hair. That is their dream. Other people find it tedious or even hate it.

Some people love x. That is their dream. Other people find it tedious or even hate it.

If you are following your passions you will discover that there are things that you find deeply satisfying.

Not mentioning that in the last years we have seen a steady rise in middle aged men who would love to work in a "My Little Pony" game :D hahaha

Why not check http://www.gamedevmap.com/, go to the Careers page of various companies, and see what jobs they offer?

They always post job duties on recruiting pages so you should also be able to decide for yourself what sound tedious and what does not.

L. Spiro

I had to work on a virtualpet game and first I was like "Really?" but then it turned out to be nice. You could throw the ball to the cute dog and he would run for it like in Nintendogs, but we had a fun debug version in which the raycast would give a headshot in the dog! We even had an animation of him dying. Naturally that didn't make in the final game.

There is another point here. With the rise of indies and mobile development you also might find yourself in a position of generalist having to deal with a bit of everything. And when you look out for job, you might get opportunities outside of your initial choice.