Please note that these are in no particular order. I had a hard enough time narrowing it down to just 5 pencils, let alone put them in order. ;)
Dixon Oriole #2:
I remember using these in elementary school with fond sentimentality. I've never had an issue with these "budget" pencils. I've noticed a lot of other online reviews on Amazon, other blogs, etc. give them a much undeserved thrashing. Even the newer Indian made pencils are high quality, in my experience. I have a few boxes of the old US made ones and a few boxes of the new Indian made ones and I've noticed no real drop in quality. The leads are well centered, the pencils are not warped, and the lead is very smooth with good point retention. They are also very durable. My first time using one since elementary school was when I found one in a parking lot a few years ago that had obviously been run over and abused. Its eraser was shot, but there was a lot of wood/graphite left. I left it in my car and used it to jot down gas mileage notes for years. When I started getting more into pencils seriously again, I took it out and began using it more regularly. Even though the paint is cracked from being run over, the graphite itself is still perfectly fine. Note that the paint is usually very thick and glossy, and does not suffer from cracking unless run over by a car! I use it on a daily basis for random notes at my desk at home. I highly recommend giving these pencils a try and trying not to take the other naysayer's opinions before giving it a chance. These can regularly be found for around $2 for a box of 12 on Amazon.
This is one of two packs of pencils that I received for my birthday from my wonderful girlfriend (Thanks!). These are just around half the price of the famed Blackwing pencils, but write just as well. Smooth, dark graphite with decent point retention. Well balanced since they do not have the heavier ferrule/eraser at the end, like the Blackwings. I highly recommend these if you can live without the nicer eraser of the Blackwing, as they are much cheaper. They can routinely be found for around $12.95 on Amazon.
Staedtler Norica HB/#2:
Let me preface my choice of the Norica by saying that this opinion is for the pre-2015 versions of the Norica, with the thicker, smoother graphite cores. The ones made in 2015 and later are not as good as the older versions. The 2015+ versions have more tooth to them and the cores are not as thick. I have yet to see ones with copyright dates of 2016, so I hope they get their act together and go back to the old cores for subsequent versions. The 2014 and prior versions are buttery smooth and dark, but with a slight tradeoff in terms of point retention. I recently found a few 2014 boxes at a lesser visited Staples out of town, and if you look hard enough you can still find the older versions on eBay. These come in Blue and Black, and I notice no difference between the versions. When I last ordered a pack on Amazon about a month ago or so of the blue ones, they were from 2008 and very smooth. Here is a link to the blue ones: Amazon. Also, if you have a Staples nearby, check them out and see if you find any with copyright dates of 2014 (or earlier) and get those instead. They come in packs of 36 there for under $10. I'd avoid the 2015 models.
Mitsubishi Hi-Uni 2B:
The Hi-Uni, like the Palomino HB and the Blackwing pencils is a premium pencil. They come without an eraser, but the lead is smooth and the point retention is very good for having such a soft and dark core. These are originally intended to be used for drafting and sketching, but work great for writing as well. Most of the time when it comes to Japanese pencils you have to order them from a seller in Japan and wait 1-2 months for them to arrive. Amazon currently has them in-stock and fulfilled by Amazon and eligible for prime, so you won't have to wait as long. They are currently around $16 for a dozen: Amazon.
Palomino Blackwing 602:
This was the 2nd of two packages of pencils that I got for my birthday from my girlfriend. These have a very similar core to the Palomino HB (and could very well be the same, as I can't tell much of a difference). They have a nice gunmetal colored finish and a very handy eraser that is extendable and replaceable. These are the most expensive of the bunch, but very much worth it if you are looking for a high quality pencil and price isn't as much of an issue for you. I noticed that at the time of posting this they are being fulfilled by Amazon, but you usually have to pay for shipping. Grab them while you can and take advantage of the free shipping! They are around $22.95 for a box of 12. Amazon.
Tombow 2558 HB:
Fantastic writing pencil, but difficult to find without having to import them from Japan or pay a higher price for them individually on Jetpens. If you're okay waiting a bit, I highly recommend these. Amazon.
Paper Mate Mirado Classic #2:
The core in these pencils is one of the best I've ever used. Smooth, dark, and with fantastic point retention. The only thing holding them back from being in my top 5 right now is the poor quality control I've found. Some pencils have erasers inserted improperly, off-center leads, and warped pencils. When you find ones that are put together properly, they're some of the best. Heck, even the ones that are slightly off are still way better than most pencils out there. And they're cheap. Amazon. Also, if you can find some older American made ones, I'd recommend those higher.
Dixon Ticonderoga Laddie HB/#2:
These pencils are thicker than a regular pencil, which makes them very comfortable to hold for long writing sessions. The core is also very thick and dark, but the point retention is not the greatest. These pencils write more like a 2B/3B in terms of softness/darkness. The eraser is oversized as well and works great. The biggest drawback to these pencils is the fact that they are larger, they do not fit in most pencil sharpeners. The only one I own that fits it properly is my little Staedtler tub sharpener, that sharpens it to a stubby short point. I love using these for crosswords, as darker cores work better on cheap paper in my experience. Find them on Amazon for under $4 for a dozen if you have a larger sharpener: Amazon.
Mitsubishi Uni NanoDia B:
I found these pencils on Jetpens (no affiliation) for around $1 a piece. They write dark, and have good point retention due to the formulation of the graphite core. My biggest issue with these is the lack of availability. I've yet to find another store aside from JetPens that sells these at a reasonable price. They are twice as much on Amazon. I also like to use these for Crosswords with smaller boxes.