Rarely, myself. I prefer to sit and wait between bedding and feeding sites. I can usually prepare for the shot, have a much better rest (my knees), and am not winded/out of breath.
However, the first deer I ever shot, with a flintlock no less, was by stalking. I had sat in the morning and had no shots. Spent midday hiking up a mountain and chasing a large herd through some laurel down the moutain. The forest opened back up to mature hardwoods and I jumped the deer several times more. One doe made a mistake by coming around in a circle. I dropped to one knee and she fell where she stood 22 yards from my muzzle. 8-12 inches of soft snow made the stalking 'easy' to stay quiet.
On one other occasion in this same spot I was scouting and was able to stalk up to two yearlings (6-months) within abou 40 yards. It was windy that day and I think these two were a little less wary than adults.
I have since done some stalking/still hunting. But my problem is I'm much too impatient and tend to walk too quickly. Wet leaves or snow and I feel more confident.
Bottom line is the deer have far superior instincts and are alert to your presence by sight, sound, and smell (always stalk into the wind) so they have the advantage. It's really a matter of keeping with it and waiting for the deer to make a mistake by coming back around or pausing just a bit too long in an opening. No question it can be more rewarding that sitting and waiting--you feel you've earned your game.
Yesterday was super windy here in central PA so I took my .44 S&W 629 for a walk. I did jump 3 deer, but not where I was expecting them (in thick scrub oak), so I wasn't prepared. I'm not sure I could have taken a shot if I'd had my .54 with primitive open sights, anyway as the shot would have been running at 50 yards and I'm not confident off-hand or at moving targets at 50 yards.
In the last 2 years, I've seen 2-3 articles on the Benoit family (father and 3 brothers) from northeastern Vermont who are literally world famous as stalkers of monster bucks. These articles have been in outdoor life, field and stream, american hunter, and/or other hook-and-bullet magazines. These guys are masters at getting big bucks every year just by putting the miles on.