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Chainsaw: Heavy and difficult to repair yourself(non-GRA chainsaws are quite uncommon and without Jury Rigging requires other chinsaws or Rippers), but it has the DT/DR ignoring thing going on for it. 80 DPS at 100 Melee, no perks.
Chance's Knife: Concealable, lightweight, mediocre base damage, high DPS, easy to repair and high crit chance. Its damage is boosted by both the Cowboy perk and Honest Hearts Grunt perk. Best of all? It's available pretty early on, near the Tribal Village north of Goodsprings. Worth braving cazadores for.
Knock-Knock: The token all-around good, but not great weapon. This silver fire axe can be found in the Searchlight Fire Station. Get the key from Logan, who will be in the basement of one of the ruined churches.
Thermic Lance: The bigger brother of the chainsaw. They're pretty rare, but you will occasionally find them in merchant inventories(Knight Torres seems to stock them commonly). At 100 Melee it has 100 DPS with no perks.
Oh, Baby!: A unique super sledge that at first glance appears to be the end-all, be-all melee weapon with its high base damage and attack rate. Then you start noticing it degrades very, Very, VERY fast and repair are expensive as hell for it. With Jury Rigging you can get by, but it constantly needs repairs and if you don't have Raul with you you'll probbly see it drop below the 75% threshold within a single battle. But it's still really, really powerful.
DLC melee weapons worth mentioning:
Blood-Nap(Lonesome Road): Better version of Chance's Knife with an odd +10 Sneak bonus, basically. The only downsides to it are that it isn't affected by the Grunt perk like it's "cousin" knife is and it requires advancing through the Lonesome Road a bit to acquire. After completing the Launch, you'll find it in a lamp post near the exit out of Courier's Mile.
Protonic Inversal Axe(Old World Blues): Think of it as a cousin of Knock-Knock with a mild EMP effect(a flat +20 DT/DR ignoring damage) thrown in for good measure. It's good, but not great. You can find one in Little Yangtze, X-13, and the Cuckoo's Nest. Note that while it's not a unique weapon, it's available in extremely limited quantities so companions should never touch it.
Old Glory(Lonesome Road): This flag pole has a mediocre base damage, but when it crits it crits HARD. A critical hit will deal almost triple damage and basically being a reskinned baseball bat, you can swing it pretty fast. Acquired from Ulysses and clearing Lonesome Road.
War Club(Honest Hearts): You don't know fast until you've wielded a war club with the Honors mod. With the mod, Slayer, Melee Hacker, Ain't Like That Now(LR), and a bottle of Rushing Water(LR)? Chances are reasonable that you can't press the attack button fast enough to attack as quickly the game allows you to. It's base damage is meh, but HFS you can attack fast with it.
EDIT: Lol, forgot my personal favorite.
Gehenna(Gun Runners' Arsenal): In terms of raw damage it is a bit behind Blood-Nap, but it has four times the durability and only requires a bunch of money to acquire.
I'll get Knock Knock the next time I play. Thanks. ^_^ How do I get Oh Baby? Sadly, I don't have any DLC. I'd get it if I had a better connection. That reminds me, I heard one of the DLCs have a Katana. Which one?
I'm a furry, and I'm proud of it! I love Lucario! ^_^
The best non-DLC melee weapon is the Machete Gladius. You can find a few Legion guys that have one at Cottonwood Cove. The DPS is not as high as Chance's Knife, but the DAM is higher.
With DLC, the best is the Gehenna (with the Pyromaniac Perk). Although, if you have to fight a deathclaw with a melee weapon, use the Blade of the West; for it's Mauler attack (requires melee skill at 50) will knock them off their feet and allow you to finish them off easily.