For shows, Victoria's Secret is my go-to. They make a lot of no-line panties that are super-comfy. I'm talking about the 5 for $25 types- I usually go with boyshorts [I believe that's what they're called?] or any other ones that are realllly comfy for me.
But, otherwise, a lot of companies do make the no-line types of underwear, as has been mentioned. =]
It doesn't bother me. I just don't wear skin tight riding pants (like legging type pants) out in public. But I don't really care if you can see an underwear line. If it bothers you though, they make some specially for riding!
Hmmm this made me laugh. The first time I put breeches on...to try them on in a store and I ahd to come out of the dressing room...worst moment of my life. I had my sweatshirt tugged way down to cover the booty that I don't have(I have been told I have a guy butt lol). My horse trainer, he's a guy, saw me and went,"could you pull your sweatshirt down any farther? I mean there's so many guys in here that wanna see you shake that thing!" he said it so loud and there were 3 teenage guys in there watching me lol. Now I don't really care who sees what. I even go to wal-mart in my breeches and boots now. And it helps that my breeches are saggy in the back. =)
Haha I don't even pay attention to which underwear I wear underneath as long as they are comfortable. They're just panty lines! I've worn my breeches just about everywhere that I've worn jeans. I've worn them to my college classes, in the mall, in gas stations, to friends houses, around campus, you name it...haha
EDIT: I wore them into work once to get paperwork and the secretary was like "wow those are big boots" and I laughed and agreed. And then she said "those pants are interesting, what are those patches for???" hahahaha then I explained to her about the horses :)