Browning BLR - I carry chambered, and use the half-cock position, with the hammer spur folded forward, a truly good safety system, IMHO. The act of placing the hammer to full-cock unfolds the spur to firing position, so it works the same way as a traditional lever rifle's half-cock feature; no separate motion required.
Marlin lever rifle, with crossbolt safety: I loathe this type of safety, or more precisely, its location, and don't use it, except as an unloading aid. In brushy country, this type of safety can be bumped, changing the position of the safety. I may eventually get the kits that replace these safeties with a dummy screw.
Ruger No. 1 - I use the tang-mounted safety, round chambered, but since this safety does not, mechanically, do as much to prevent a round from being fired, I trust if less, and am more likely to have the chamber empty when moving. It depends on how rough/cluttered the terrain.
Winchester Model 70 - This is an excellent, ergonomic safety, that disconnects the firing mechanism. I trust this safety more than any other, equivalent to the 98 Mauser, anyway, and have no problem keeping a round chambered when moving. Dropping the weapon, or a blow to any part of the weapon, cannot cause it to fire. A derivative of the Mauser 98 design, these weapons had to be safe for soldiers to carry chambered while in battle.
Ruger Mini-14 - I am a lefty, and love this safety system. I have no problem with keeping a round chambered while moving.
AR15 - I hate this safety. It is ready to fire, with the "dingus*" down. I trained myself for two decades that when a safety lever is pointed downward, the weapon is on-safe, which is true of pistols I used in the past. Then, I take up the AR15 system, and find a safety that is ready to fire when the lever is vertically downward. While the MOTION of off-safe-ing an AR15 is natural enough, the vertical lever can cause me a crisis of confidence, no matter how much I train. One time I did a dynamic entry with an AR15, and this crisis of confidence surfaced. I don't plan to ever do so again. I have elected myself to be the shotgun guy, or the boltcutter/prybar guy, for the rare occasions I have to do this stuff. (Our SWAT team does most dynamic entries; we patrolman only do this if death or injury is imminent for people within.)
Remington 870 - I prefer to unlock the action, and keep it slightly open, or empty the chamber, rather than trust the safety. I won't trust a mere crossbolt. There are times I will RUN while carrying with a round half-chambered, and the action partly open, because I use a couple of these weapons on police patrol. When I have to really pour on the speed, I will grip the forend and barrel together, hard, with the chamber halfway open. When the guns ride in a vehicle, or are slung, the chamber is empty.
*Col. Jeff Cooper's term for a slide-mounted safety lever typical of the Beretta M9/M92 and S&W 1st-3rd Generation autopistols.