Which brand(s) have the most sturdy landing gear?

I find it relates much more to the size of the model.

Yes and how much weight you had to put in the nose to prevent tail sitting.

Hasegawa...2nd would be Tamiya...

Well you said it, anything but Revell kits has strong gear. All F-105 kits in all scales seem to have weak gear though, and thats more of a poor design where the gear attaches to the upper wing half, rather that weak gear legs themselves. 

Testors 1/48 O-2 has very weak main gear.

Just a note on attaching the landing gear;  I usually use CA or epoxy to glue the tiny attachment points on landing gear because  styreene cement melts and softens the plastic causing further weakening problems .

It definately depends on what scale you're building, strength by design, and or weights if needed (Tricycle landing gear).  If worst comes to worst, you can always opp for some AM metal landing gears.  This should solve most problems.  I hope this helps.

Toshi