I'd like my boards to look and feel the best as they can, particularly for photos. I invest a lot of effort and attention in the detail and look of my boards, but that's not enough if the end result, components and all, does not look as polished.
When I solder through-hole components, I will typically cut the lead, or anything poking out, together with the solder blob as close to the board as possible using flush cutters. (Using flush cutters is important since regular cutters taper in for the cutting edge, which does not allow cutting as close to the board as needed.)
You'll be left with a rough surface that needs to be touched-up with an iron. Sometimes that's all it takes, but often you'd want to add some solder to create a nice dome. If it didn't work out, cut off the abomination and redo.
When I'm happy with how the solder points look, I clean the burnt flux with Flux Off. The board can become a bit sticky after that, so give it a good clean afterwards. You now have a beautiful board with smooth solder points!
Here's a video I've made of the process
In the video it looks more laborious than it really is once you get used to it. The one thing to be careful of is to not cut off the soldermask when cutting off the blobs!