OK, there are a number of ways to answer this question.
#1 – Let the computer decide. People have said make a Pandora station…I also have a Zune, and the latest version of their software has a “smart DJ” function, where you create a smart DJ based on an artist, and it will pick music similar. How it decides, and how that is different from Pandora, I can’t say, but here’s the list of what it came up with:
Urge Overkill, Foo Fighters, Hole, Pearl Jam, Green Day, Oleander, Alice in Chains, Mudhoney, The Breeders, Weezer, Bush, Papa Roach, Babes in Toyland, Oasis, Presidents of the United States of America, Pixies, The Beatles & Redd Kross
Now this seems like an interesting way to pick artists…OK Hole…married to the lead singer, and Live Through This sounds as though Kurt Cobain practically wrote it for Courtney Love. Foo Fighters, you have the drummer from Nirvana, makes sense. Bands like Alice in Chains, Mudhoney, The Breeders, Bush…those are kind of in the same time period, all part of the “grunge” scene. The Beatles are an obvious influence, and the closest you’re probably going to get in terms of their signature sound is the Pixies, probably the single best pick on this list. I liked Oleander, but they came after Nirvana and sort of co-opted their sound, which is probably the second direction you could go.
If you’re just looking for the sound, Oleander is a good choice, Puddle of Mudd is a blatant Nirvana rip off, Seether does a great job of sounding like Nirvana, but has more originality than Puddle. Look at just about anyone who was popular in 1995, and you’ll find a Nirvana ripoff, Silverchair is a good example. More recently the world has been saddled with Nickleback. Or even more obscure, Earshot, Dogs Eye View, For Squirrels, Our Lady Peace, Candlebox and Saliva. And then of course there is the abomination that is Creed.
Now for the third way to make this comparison…my way, which boils down to influence. Kurt Cobain was heavily influenced by the Beatles for one…he wrote About a Girl after listening to one of the Beatles early albums for like 3 solid hours. Smells Like Teen Spirit was actually admittedly an intentional Pixies rip off, he felt such an affinity for the Pixies, he thought he should be in the band. Of course, the opening chords of Teen Spirit belie a deep respect for classic rock/arena rock of the 70s…much of Nevermind was written in a style somewhere between Iggy and the Stooges and Aerosmith, but the opening licks of Teen Spirit were basically the bridge from Boston’s “More Than a Feeling” turned on its head. Cobain was influenced heavily by Zeppelin, Queen, Sabbath, AC/DC and Kiss, which gave his music the harder edge, but underneath that, he incorporated a lot of more underground influences. The Melvins might be Cobain’s single biggest influence, but he also loved Sonic Youth, Black Flag, The Butthole Surfers, Captain Beefheart, and many others. Then of course there were the new wave influences like Devo and Blondie, punk influences like the Clash and the Sex Pistols, progressive/indie bands like REM, and pop influences like the Knack and yes, even the Bay City Rollers (the gloss you hear on Teen Spirit was inspired by such upbeat, yet shallow pop). But most importantly was that Nirvana steeped its music in the early blues influences, people like Robert Johnson, Muddy Waters, and Lead Belly.
So, for my money, I’d go to some of his most obvious influences, the Pixies and the Melvins, early blues recordings, and bands that were also steeped in the blues….Sabbath, Zeppelin, and more recently the White Stripes (or anything Jack White has a hand in). I think the way to capture the truest essence, the feel of Nirvana is to find the bands which share Cobain’s muses (or the ones that were Cobain’s muses). But if you’re simply looking for co-opted sound, there are many copycats, and of course computers can find common threads and make suggestions.