Cybercore????
Gradius V is tops, and I really can't think of a horizontal shooter I like more, but it's awfully long and the lack of a tricky scoring system keeps me from playing it often. Which is pretty much what a few other people have already said.
I prefer vertical shooters, though, so there are a bunch I think are better than Gradius V. You want:
Just about every Cave game - You'll want to start with DoDonPachi. It's probably the best shooter ever made (I'd say "definitely" but I'm soo burnt out on chaining) and it's playable in MAME. There are also a half dozen or so other Cave games in MAME, and they're all excellent but I much prefer Cave's recent work to any of them. The scoring systems in Ketsui (not yet emulated and no console port, unfortunately) and Espgaluda (if you have an import capable PS2 BUY THIS NOW) are very free and fun, with none of the frustration that comes from totally hosing your score as a result of dying. Their systems are also much easier to grasp than MAME'd stuff like ESPrade or Guwange, which I love but am still somewhat baffled by.
Dodonpachi DAI-OU-JOU is the only other recent Cave game to get a home port. It is one of the hardest games ever made. If you're new to score gimmick shooters I strongly suggest not buying it. Actually, but it. But don't play it. It'll hurt you. Still better than Gradius V if you're into sickie kicks.
Oh, and Progear's in MAME now, isn't it? I dunno if it's well emulated, but if it's anywhere near arcade accurate it's a ton of fun, and the only hori I've put considerable time into that's on par with Gradius.
Armed Police Batrider - Also available in MAME. One of my top 3 shooters. Tons of secrets, characters and fun, simple scoring. It's also very colorful and you can see the bullets easily, so it's better than Battle Garegga! (I'm sorry all you BG luvvers, but I'm one of those folks who can't stand the tiny bullets and the shrapnel and the brown. I keep thinking I'd enjoy it more if I could play it in a cab, but I'm not going to spend $100 to find out.) I think pretty much every Raizing shooter's emulated by now, and they're all worth checking out for yourself as opinions divergent on which are the best. But for me it's Batrider, then Dimahoo, which has the greatest attract mode in the history of games.
Gunbird 2 - (Or any vert Psikyo shooter as they're all the freakin' same) Funniest endings ever. The whole coin score system's kinda irritating but I find the game so fun I don't care. Also hard as hell -- I really suck at Psikyo games for whatever reason. Has a DC port, a not-as-good PS2 port, and I think it may be emulated. Other worthwhile Psikyo stuff: Dragon Blaze (PS2 port comes out this month, but it'll probably have the same icky lack of lo-res that plagued the other Psikyo packs) which is Gunbird with dragons; the Strikers games, which are Gunbird with fighter planes; and Space Bomber, which isn't much like Gunbird but is very funny and cute.
Ikaruga - Everyone's played this by now, haven't they?
Mars Matrix
I know I'm forgetting something...
I've barely played Border Down. My DC stick is all busted and I can't bring myself to play shooters with a pad nowadays. So I dunno if it's better than Gradius V, but it is worth buying. I know it's supposedly a total bitch to find nowadays but I got a copy offa ebay for $40 or so a few months ago...Maybe I got lucky?
Shikigami no Shiro 2 got a US PS2 port. I think it's called Castle of Shikigami 2? (Kinda sad that I'm not sure, since I own it...) Not the best home port of the game, and I'm not all that into it, but it's $10. Who cares if it's not better than Gradius. It's TEN DOLLARS.
Gradius V is better than Radiant Silvergun. It is sooooo much better than Einhander. Mentioning R-Type Final in the same thread as GV kinda makes me feell icky. And it totally trounces all that 16-bit crap that hasn't aged well at all. Except M.U.S.H.A. I love that one.