Well, I have 2 that were noteworthy and you can try for yourself.
 
1. I was riding to a story mission, and on the way i was passing a stagecoach. For shits and giggles, I rode into the wheels of the coach and after about 5 seconds was sent into another dimension. After about 20 seconds of a blank tan screen, marston and my horse were standing where i believe the glitch occured and everything was back to normal.
 
2. Ok, try this one. Go to thieve's landing, and purchase the property that is for sale. Make a save. Then, go play poker with the elegant suit on. Then, after some time playing, get caught cheating. During the duel, shoot the gun out of the other mans hand and go save the game in the property. Now, when you go back to play poker, the other players should look low res and looks like the textures are still loading in. I won the game and the textures still hadn't loaded.

Funnily enough I haven't encountered that many glitches. I did try the slingshot into the sky in free roam found McFarlane's Ranch which is like the set of swings in GTA IV. I ended up staying at the top of the launch one time and just started sniping from up there.

the police station in blackwater became the gateway to the blue hell, people would keep walking in there and falling, when i jump in i keep falling until i hit the front steps.

" Funnily enough I haven't encountered that many glitches. I did try the slingshot into the sky in free roam found McFarlane's Ranch which is like the set of swings in GTA IV. I ended up staying at the top of the launch one time and just started sniping from up there. "

I have really fond memories of glitch-hunting in Halo 2... other than that, when I was testing Metroid Prime 3 there were some.... interesting bugs pre-launch post-beta.

This game has glitches.... lets ignore that in the reviews.

" @lilbigsupermario:  
 
http://www.youtube.com/watch?v=W5XHX91Botg      You should be able to find the building by looking at the map and landmarks in the video. It might take a few goes. Hope that helps. It also works in single player. "

When I was arm wrestling a guy right when the match was about to start he all of a pushed his chair out and stood up.  So he was just standing there and the chair he pushed back glitched up and was stabbing him through the stomach while I arm wrestled an invisible person.  Tha'ts not the best part though, after that happened I got on my horse, and I tried to feed it an apple, but every time I chose an apple instead of it feeding the horse an apple, a chair would appear and stab me in the stomach just like the guy I was supposed to have arm wrestled.  It was messed up.

If by "best" you mean, "take this broken piece of shit back to where I rented it from", I got to a point where I could only target birds.  There were several enemies right in front of my and I pressed the trigger and locked into a bird that would normally be out of range.  Also, I tried to take cover and instead started running along the walls in a circle. I wasn't pressing anything. Finally, my Special Needs horse, as I call it, ran right past me off a cliff when I whistled for it. This happened three times in a row.

Posted this in the other glitch thread as well.
 
Dead eye + dynamite = missile
 
 http://www.youtube.com/watch?v=7DZzsJ-svGw

On the first mission with Landon, I ran into an odd...event.
 
Him and I were walking, and while we were talking he started FIRING REPEATEDLY AT SOME HORSES. Nobody acknowledged it, and the conversation went as it should while he was just unloading lead on these animals. The horses wouldn't die, and then a cutscene started. After the cutscene, we get on the horses he was shooting at. 
 
:-|

"Posted this in the other glitch thread as well.
 
Dead eye + dynamite = missile
 
 http://www.youtube.com/watch?v=7DZzsJ-svGw "

" Posted this in the other glitch thread as well.
 
Dead eye + dynamite = missile
 
 http://www.youtube.com/watch?v=7DZzsJ-svGw "

" Posted this in the other glitch thread as well.
 
Dead eye + dynamite = missile
 
 http://www.youtube.com/watch?v=7DZzsJ-svGw "

only one i encountered was where i was during a mission for ricket. during the cutscene, we were sitting at a table and some random npc clipped through ricket and sat in his seat. throughout the whole cutscene the npc was moving his mouth as if he was talking and ricket was clipped through him actually talking. very wierd.

To be fair I have not had many glitches.  I recorded this one from yesterday. 
 
 Walking through Armadio stumbling upon a bouncing wagon cart.  
  

I don't  know if anyone has experienced this but after the mission where you fire the cannons and capture the first of your ex-gang members I went back to my house in   
Chuparosa and after I had saved, everytime I left my room people would start shooting at me and a gunfight would break out in the town. Not sure if this had anything to do with what happened next, but strange anyhow.   
  I sat down to play poker, from the cards being dealt there were clearly 4 people at the table, but one of them was invisible, and another was sat not at the table but in his chair pushed way back on the other side of the covered area outside the bar. Also when one of the players dealt the flop all the cards would be placed in a pile, rather than side by side, so you could only see the uppermost card - very strange. I think the continual gunfight might have disrupted the game somehow, as bullets and people were flying back and forth all through the game. 

I hit R1 to take cover but marston bounced off the wall and was launched 40 meters in the air, followed by falling to his death.. 
 
It's as if i was flying a plane in San Andreas and then jumped out and didnt use the parachute, except it was Marston instead of CJ

I encounted a silent cougar. That wasn't cool. Usually you can hear they're growls and switch to dead eye to save yourself. This was a sneaky one.
 
@JamesK:
Dude, that's so gangster. That guy is so far ahead of his time.

The one I've seen the most is the hydraulic stagecoach thing where the horses are basically stuck in the ground, can't move while the stagecoach just bounces up and down.  If it weren't for the skipping checkpoint feature they put in, I wouldn't have been able to complete certain missions.  I'll have to wait until they fix this glitch so I can do the missions over again and finish them properly...don't think I missed anything important, but still feel like doing them over.  I hope this doesn't get in the way again because I still have plenty of missions to complete I'm sure.
 
Other than that, there was this weird glitch when my brother was playing.  I can't remember what town he was in, but somewhere in Mexico...he was just staying in this one building trying to get as high a bounty as possible.  It got up to around 2,500 when he decided to flee from the cops (after he had killed seemingly hundreds of them, but of course they keep coming).  He fled on horse and without thinking jumped off a cliff going full speed, and as soon as he landed the horse died and then the game started running at like 10 fps.  It wasn't until he got away from the police and the "Wanted" meter disappeared that it started running at its normal framerate again.
 
I've also had my horse drop dead for no apparent reason at certain spots.  My friend theorized that this only happened with the skinnier horses if you pushed them too hard, but it happened to me a few times and I'm pretty sure it's just a funny glitch.

I was standing near the bottom of a cliff, I called for my horse and dukes of hazzard style the horse came jumping off the cliff and died in front of me as it hit the ground.

One that pissed me off was when I shot beavers, raccoons, and skunks, they disappeared when shot so I couldn't skin them.

This one totally freaked me out ENDING SPOILERS

- The taxi stagecoach fell in a river. 
- Button prompts that went missing.
- Stretchy arms when I was riding my horse.
- Textures that went missing which made it look like a cell shaded game.
- Getting catapulted 20 meters  in the sky for no reason and dying.
 
Seriously, I've never played a game this glitchy.

I've only encountered two glitches so far and they've only appeared in multiplayer. A lantern was suspended in the air in one of the gang hideouts shot it, made a big boom killed some gang members. The second one was just seeing a horse bounce up and down like the video above without the carriage part.

Best glitch was after I downloaded the DLC.  I was able to get 500xp free by starting a gang fortress battle, and 10 seconds later it said clear and I got the xp without having to do anything.  I went to level 50 three times that day.  Now I have to legitimately grind to 50 two more times for the last legendary mount.

I've only had one glitch occur in the game and that was a dude riding his horse by me, and his had was stretched up about 20-30 feet.

" Best glitch was after I downloaded the DLC.  I was able to get 500xp free by starting a gang fortress battle, and 10 seconds later it said clear and I got the xp without having to do anything.  I went to level 50 three times that day.  Now I have to legitimately grind to 50 two more times for the last legendary mount. "

Best glitch in-game for me was when I was too slow to help a lady of the night in Mexico from getting gutted with a knife. The dude knifed her, I shot him, and then she was convulsing on the ground and going around in circles for about 2 minutes!

I saw a wagon just randomly fall off a bridge that i couldn't have fallen off of, gave me a WTF moment 

I saw a wagon just randomly fall off a bridge that i couldn't have fallen off of, gave me a WTF moment 

I've been loading up an old save and going to shoot the crap out of people. In McFarland's Ranch I was trying to blow this dude's head off when he ran toward the shop and magically fell through the boardwalk. Another time, I'd gotten a bounty outside of McFarland's Ranch and then rode back in. When you do that the first time, it cuts to a stationary shot of the train station with a bunch of tutorial text about paying off your fine. I had just clicked into Dead Eye right as it started that, so as the tutorial text rolled Dead Eye kept flashing on and off really quick. It even had the sound effect. Woosh-wosh woosh-wosh woosh-wosh over and over again. When the tutorial text stopped, and it cut back to me, it kept doing that, but at a slower rate. Finally after it had "auto-clicked" into and out of Dead Eye twice it stopped. 
 
Oh, another one. It's not really a glitch, but when you come across one the wagons with the workers in them, look to see if one of the workers is lounging in the back of the wagon. If you shoot that one, he will literally get up, walk out of the wagon, and fall to the ground dead. It's fucking hilarious.