Hand-knitting in the 18th century seems to have been confined to objects such as stockings, hats, mittens or gloves, and the occasional knitted undershirt. These objects all have one thing in common: they need some stretch, and need to fit odd shapes well. Items such as scarves, shawls (wraps), etc. were not knitted in the 18th century.

There is some debate in 18th century reenacting circles about the proper gauge of 18th century knitting, but I think that question is misguided -- the answer will vary depending on the item being discussed (see the paragraph here on the gauge for period stockings). Period stockings were generally knitted with a gauge somewhere between 7 stitches per inch all the way up to 30 or more stitches per inch (with the finest gauges being knitted by machine), with many examples in the 9 to 15 stitches per inch range. Some surviving examples of period hats and mittens, on the other hand, seem to have been knitted in a larger gauge.

Tools:
Yarn

Knitting needles (aka knitting pins) in the finer gauges were usually made of steel wire. The larger gauge needles used by Scottish bonnetmakers seem to have been made of wood.
Modern nickel-plated steel double-pointed knitting needles from Inox or Skacel are available from various vendors and look very much like period needles; or you can purchase reproduction knitting needles from Wooded Hamlet in sizes #000, #0, and #1.

Knitting sheaths of various sorts were used throughout the British Isles and Europe from the 17th through the 19th centuries (Rutt, pp. 20, 125-126). They held the knitter's working needle, freeing that hand to throw the yarn more quickly. Primitive examples could be made from hen's feathers bundled together with string, or bundles of twisted straw; finer versions were made of silver or fine woods like mahogany.
Links:
- A collection of 18th and 19th century knitting sheaths at Times Past Antiques
- A history of knitting in the Dales
- Some 19th c. knitting implements at The Library Company of Philadelphia
- A collection of knitting sheaths at Brecknock Museum & Art Gallery

Whisks or knitting belts were used by production knitters in the Shetlands in the 19th and possibly the 18th centuries to speed up the knitting process. A picture of a knitting belt in use is shown here. Reproductions can be purchased from Journeyman Leather and Four Seasons Knitting.

Stockings
See 17th & 18th Century Common Stockings and Chart for 18th Century Stockings

Men's Knitted Caps & Scots Bonnets
See 17th & 18th Century Knitted Caps & Bonnets

Mittens and Gloves
A knitted mitten is shown on p. 189 of Collector's Encyclopedia of the American Revolution by George Neumann.  This appears to be in a fairly large gauge -- possibly 5 to 6 stitches per inch.  Similar mittens, knitted from undyed wool, were recovered from the wreck of the General Carleton, along with a glove very similar to the Gunnister glove (below), except that it has two rows of fringe rather than the purl stitches which decorate the Gunnister glove.

A pair of heavily fulled gloves was found with the Gunnister bog body, which dates to the late 17th century (see Pulliam, cited above).  The gauge of these gloves is 17 stitches and 14 rows per inch (i.e., they were knitted at a larger gauge and then shrunk to size). More thorough descriptions of the Gunnister items (caps, pouch, stockings and gloves) and Scots bonnets can be found in Early Textiles Found in Scotland and Stuart Clothing and Other Articles from a late 17th Century Grave at Gunnister, Shetland by Audrey S. Henshall, in the Proceedings of the Society of Antiquaries of Scotland, Vol. 86, and in Gunnister Man's Knitted Posessions, by Deborah Pulliam in Piecework, September/October 2002.

A pair of knitted elbow-length, fingerless linen mitts, dated 1787, is posted on Karen Augusta's website.

Waistcoats
There is some evidence for knitted men's undershirts (called waistcoats, but worn underneath the linen shirt) in the 17th and 18th centuries. The most famous example is the silk undershirt worn by Charles I to his execution in 1649.  Several so-called 'Florentine Jackets' survive in various European collections, and there are references to them in period documents from the 17th through mid-18th centuries (Rutt, p. 81; Fashion in Detail by Avril Hart and Susan North, p. 184-5).  These were knitted in five rectangular shapes (one for the back, two front pieces, and two sleeves) and shaped during assembly.

A knitted women's jacket dating to the late 17th or early 18th century is in the Victoria & Albert Museum's collection (Hart & North, p. 186-7); such jackets may have been worn for casual wear around the house and during convalescence after childbirth. The same book also shows (p. 188) a knitted petticoat, with more than two thousand stitches cast on for the hem. I don't, at present, know of any knitters insane enough to try to duplicate it.  It may have been made for a guild, and has never been worn.  A similar petticoat is in the collection at LACMA.

Two knitted infants' jackets are shown on page 159 of What Clothes Reveal by Linda Baumgarten; these probably date to the late 17th to early 18th centuries.  A mid-18th century baby's jacket knitted in cotton is shown on p. 26 of Helen Bennet's Scottish Knitting; similar jackets are in the collection of various museums, including the Victoria & Albert Museum.

Other Items
There is a tantalizing reference to stocking sleeves on an old wool flannel jacket in a runaway ad in the Maryland Gazette, Sept. 13, 1770. (Baumgarten, p. 127)  A knitted sleeve or stocking leg was found in the wreck of the Mary Rose (1545) (Rutt, p. 65), but given the lack of evidence, it's impossible to know what any 18th century knitted sleeves may have looked like. Helen Bennet (p. 4) refers to knitted sleeves being knitted in the southwest of Scotland, but doesn't cite a particular date.

There is a reference to knitted garters circa 1711 on p. 88 of Rutt.

Pincushions of various sorts were knit, usually in silk. Here is an example of an English pinball from the early 19th century with Quaker provenance, offered for sale at http://www.samplings.com/.

The Gunnister bog find also included a knitted pouch.  I don't know of any other surviving examples of 17th or 18th century examples of knitted pouches, though various knitted pouches are known from earlier periods, and there are numerous references to knitted purses in period documents.

Other Online Knitting Resources:
Historic Knitting List on Yahoo Groups
Free online video clips of basic knitting stitches at http://stitchguide.com/
Knitting Tips and Information for Re-enactors by Phyllis and Paul Dickinson -- there are a few points that need clarification. For one, ribbing IS period, but not at the tops of stockings -- stockings with 3/4" wide ribs running the length of the stocking were worn. Secondly, larger gauge knitting was known for caps and mittens.
Knitting tips and tricks at Maggie's Rags|
Knitting with Handspun Yarns -- has tips on calculating yardage
Fiber & Yarn Conversion Chart

Books on Knitting:
Folk Socks by Nancy Bush-- not a book on period knitting, but can help with reconstructing period knitting techniques; see comments on this book in the Historic Knitting List archives
Knitting in the Old Way: Designs and Techniques from Ethnic Sweaters by Priscilla A. Gibson-Roberts (Caveat: sweaters as we know them in the 21st century were not worn in the 18th century, but knitted vests or waistcoats were worn as undershirts under other clothing for additional warmth. I'm including this book because I like it and it helps clarify some older knitting techniques)

References:
Bennet, Helen. Scottish Knitting. Shire Album 164. Shire Publications Ltd., Cromwell House, Aylesbury, Bucks UK, c. 1986.
Babits, Lawrence E. Eighteenth Century British Sailors' Clothing in Back to Our Roots II: Investigations into the Influences of Immigration and Trade on the Development of 18th Century American Dress, Tidy's Symposium Papers, March 20, 1999.
Burnston, Sharon Ann, Fitting and Proper
Dunleavy, Mairead, Dress in Ireland
Farrell, Jeremy, Socks & Stockings
Gehret, Ellen J., Rural Pennsylvania Clothing
Henshall, Audrey S. Early Textiles Found in Scotland and Stuart Clothing and Other Articles from a late 17th Century Grave at Gunnister, Shetland in the Proceedings of the Society of Antiquaries of Scotland, Vol. 86, 1951-52.
Neumann, George. Collector's Encyclopedia of the American Revolution.
Pulliam, Deborah. Gunnister Man's Knitted Posessions, in Piecework, September/October 2002. Loveland, CO: Interweave Press.
Rutt, Richard. A History of Hand Knitting.

Thanks to Katheleen Manneke for pointing me to various examples of period knitting, and to Deborah Pulliam for correcting errors.

A few words on crochet and tatting: Both crochet and tatting are 19th century techniques. There are a few books around that talk about crochet and tatting dating back to the 15th century or earlier, but so far, those who have looked for or looked at the textiles in question either find that they're nonexistent or are mislabled needle lace or knotting (which are not the same as tatting), or nalbinding (which can look a little like crochet but is really not the same thing). An essay on the subject, written by someone much more knowledgeable on the subject than I am, can be found in the files of the Historic Knitting List. If you can find actual existing objects (not just a second- or third-hand reference in an arts and crafts book) made with tatting or crochet dating earlier than the 19th century, I'm sure the folks there would be happy to see the evidence.