Most of these are links to resources to help you learn a specific topic, or to a site covering a lot of ground. I'm trying to include and discussion of textbooks, and links to practice problems in each section too. If you need help with a particular problem in any branch of chemistry, ChemicalForums is pretty active, and r/chemhelp is pretty good too. A set of textbooks worth looking into if you have problems with specific areas are the Oxford University Primers, which are small, usually pretty cheap, texts which cover a small area generally very well.
12 grams of Carbon: An attempt to teach chemistry from scratch, might even by helpful at GCSE level, or as a refresher. I haven't looked at it far enough to see how detailed it gets.
Preparatory Chemistry: Chemistry for beginners. It teaches you chemistry without assuming any prior knowledge, so a decent place to start for anyone beginning a chemical education.
Chemguide: Excellent explanations on everything covered by most A-level syllabus', with notes to tell you what's relevant and what isn't. The writer also has a book available. [I'm not being paid to plug it, I genuinely found it helpful!!]
AlevelChem: Whilst there isn't much content here, it does have all the exam boards specification, in a much more accessible format than the PDF files on the exam boards own websites.
S-Cool Chemistry: Good for all subjects, easy to understand. Doesn't break things down by exam board though.
TSR:Chemistry: The Student Room has some revision resources, written by people because they want to, not because they're paid to. It's incomplete and I can't always vouch for accuracy, but sometimes a different way of explaining things really helps. The forums can be helpful too.
Equation Balancing: It's from a university, but the 'level 1' material should be easy for A-level students to understand.
Khan Academy: The sites has some nice videos on a variety of topics. Some of the content might be of interest to first year undergrads too.
Maths Notes: Possibly a little beyond A2 Maths in places, but for Further Maths it's helpful, and if maths is a weak point for you it might be helpful when revising uni level maths used in chemistry.
Chemistry Drills: Some problems aimed at those studying A-level material or that of a similar difficulty.
Beyond A-level, most sites are too specific to simply be classed as 'Degree Level Chemistry', so below it's broken down into different areas. Some sites do cover a bit of everything, so whilst they're listed by their primary areas, some do branch out.
Periodic Tables: The obvious place to start, people like different things, but this one, this one, and this one are a good place to start.
Chem4Word: A handy add-in for Microsoft Word. I've personally found it helpful, but maybe slightly buggy, so it pays to save work before using it for anything.
Chemistry Symbols in MS Word: A summary of how to insert them easily.
MolCalc: Easy to use, it simply returns the molecular mass of any given formula, plausible or not.
pKa Predictor: Draw a molecule and it'll predict the pKa for every proton present. Ignore the error messages that pop up.
Chemicalize: Give it the name of a molecule, and it'll return a structure and a large amount of data too. You can also search by most common identifiers, like CAS or SMILES, so you can get a name from a structure too.
Molecule Visualizer: Give it an IUPAC name and it returns a structure, usually pretty accurate, although may not work properly for novel compounds.
Reference Resolver: A really impressive site where you type in a reference in a sensible format and it'll redirect you to the article.
Chemistry Textbook Crawl: A blog where someone is going through their undergrad notes, it's got some handy basics on IR, and does cover some other general chemistry too.
SDBS: The Spectral Database for Organic Compounds is incredibly helpful when your own spectra are a mess. NMR's are fully interpreted, and the other spectra are good for reference. Wide range of compounds too.
Infra-red shifts: I'm yet to find a truly comprehensive list of shifts to use as a reference, but there are good lists here, here (also includes some IR theory), and as a basic introduction, this can be handy.
NMR Solvent Peaks: The worse your spectra, the quicker you get to know these off by heart, but this is a handy list of all common solvent peaks in proton and carbon NMR.
NMR Predictor: Might not match your spectrum perfectly, but really handy when you're feeling lazy and don't want to interpret a spectrum from scratch when you're pretty sure what your compound is.
NMR Chemical Shifts: This link is for proton NMR, but the top left corner has links to carbon, fluorine, phosphorus and selenium NMR, and is incredibly extensive. There's also some helpful images here.
Basic Concepts of NMR: A nice introduction to the underlying theory, and also covers some higher level material too.
IR and NMR Problems: A really good website for practising structure elucidation from IR and NMR data.
RSC Primer: The Royal Society of Chemistry has some great videos on basic lab techniques, even if their choice of background music is somewhat bizarre.
Experimental Section Checker: Really handy tool for checking your experimental sections are formatted correctly. The RSC also has a similar tool, but I haven't been able to make it work for me.
Equation Balancer: Automatically balances chemical equations, but obviously no replacement for being able to do it yourself!
Column Chromatography: Really good notes on setting up columns to get a decent separation. There's also a paper on the subject here.
Pressure-Temperature Nomograph: Provided by Sigma, it's handy for vacuum distillations, etc.
When it comes to textbooks, I've only ever used Clayden, Greeves, Warren and Wothers: Organic Chemistry, which I believe is the standard one for UK undergraduates. Personally, I've found it to be very good, and I've never felt an explanation was lacking. If you really want to get ahead in organic chemistry, it's suited to self-study too. However if you want to look for something else, there's a discussion about organic textbooks here.
Golden Rules of Organic Chemistry: It's a little simplistic, but a really nice place to start, and things everyone studying organic chemistry should know.
Substitution vs Elimination: Easy to use flow chart for determining whether a reaction is E1, E2, SN1 or SN2. Some easy to follow lecture handouts are available here.
Organic Reactions: This is a great list of organic reactions, with mechanisms and examples of uses.
Name Reactions: It's not comprehensive, but the 70 or so reactions covered are done well, with lots of detail and well-drawn mechanisms.
pKa Data: Pretty comprehensive lists of pKa values for common organic molecules
Master Organic Chemistry: Pretty much does exactly what it says. Summary sheets are really good, and show how organic chemistry is pretty logical, not a load of steps happening for no reason.
OChem1&2: A huge list of powerpoints on what looks to me like second year (in the UK at least) Organic chemistry, with some biochemistry and polymers added too. It's an accompaniment to John McMurry's Organic Chemistry Textbook. (It's not one I've used, so I won't pass comment on the book)
Freelance Teacher: I've highlighted the organic section, but there's also some videos on general chemistry too.
ChemTips: A really good resource for organic theory, practical advice and loads of other helpful stuff.
First Year Organic: There's some lecture support material here that might be handy to some people, and loads of problems to try.
Yale Organic Chemistry: Yale University have a free online first year organic chemistry course. I've not tried it, but I can't imagine a university of such standing producing anything useless.
Peter Norris: Really good material, particularly if you like your chemistry taught with a British accent.
Virtual Organic Textbook: A nice resource with plenty of material on different areas of organic chemistry, starting with the basics.
ChemHelper: Organic chemistry mechanisms, practice questions, tutorials, although the forum associated with it appears to have been discontinued.
Organic Chemistry Course Notes Archive: Written by students, for students, so I can't vouch for it's accuracy throughout, but it can be handy to have an alternative explanation from someone in the same position as you.
AsktheNerd: A surprisingly wide selection of data, covering stereochemistry, mechanisms and spectroscopy.
CliffsNotes: Covers plenty of organic chemistry. There's no obvious source of the information, but from what I've read it seems fairly sound.
SynArchive: A huge resource of syntheses of many organic molecules, would probably be really helpful for retrosynthetic analysis revision, as you can look at a molecule then see a complete route to it's production.
ChemistryByDesign: A really good site for training yourself in medium to advanced level organic synthesis and total synthesis.
Nomenclature: A good introduction to naming most functional groups you'll see in the first couple of years of organic chemistry. There's some basics covered here too.
Stereochemistry: I've highlighted the comprehensive stereochemistry notes UTDallas have, but other stuff is covered too.
MO Theory: A really good pdf of lecture notes used to introduce MO Theory in organic (and physical) chemistry.The article on p36 is a particularly good introduction to using MO over Lewis Theory.
If you can't find what you're looking for, then OCHeM and Dr Lennox have lists of some other sites available. OCHeM also has some exam questions, and all important organic chemistry songs.
For practice problems, at a variety of difficulties, several sites exist. I think this from the Evans group at Harvard is very helpful. This site has a wide range of topics covered very well, and problems are available here, here and here too. There's also this site, which covers some inorganic topics too, and EasyOChem has some material which is free, but I personally feel there's enough information about that paying for an online resource is unnecessary.
For textbooks, I have Housecroft & Sharpe: Inorganic Chemistry, which does the job fairly well, even though some sections feel more encyclopaedic than like a textbook. I've also heard good things about Shriver and Atkins' textbook, as well as Cotton and Wikinson's, and Greenwood and Earnshaw's is again more encyclopaedic, but one my tutor likes. A discussion on inorganic textbooks can be found here.
Crystal Field Theory: Some nice handouts introducing Crystal Field Theory.
Carbonyl Ligands: Some easy to understand explanations of how carbonyl ligands behave.
Solid State Chemistry: A full text book on solid state chemistry
My standard textbook is Atkins' Physical Chemistry. Personally, I find it a bit dry, and it is fairly mathematical, with some calculations jumping steps they deem trivial, so not perhaps the best for people who struggle with maths. If you do get it, I wouldn't worry about splashing out on the most recent edition, by all accounts the only real difference between issues is that material is shuffled around, with any problems found corrected. My lecturer swears by the 3rd edition, although it's now in at least a 9th edition. A discussion on other Physical Chemistry textbooks can be found here.
Gibbs Phase Rule: Reasonably well explained introduction to the Gibbs Phase Rule.
Electrochemistry: Extensive Electrochemistry notes, there's also a dictionary of terms here.
UV/Fluorescence Spectroscopy: Notes on the underlying theory.
MO Theory: Chemogenesis does a nice job of basic to intermediate MO theory, and has some other nice material too.
Polymers: Some nice material on the kinetics of polymers, and Mark-Houwink constants.