To touch briefly on their strengths and weaknesses:

PressureTreated Lumber: Southern Yellow Pine For most  projects PT wood is quite acceptable in a clear variety(#1). PT wood has a tendency for shrinkage, splitting and grain raising (all of which can be greatly minimized with proper initial sealing). The most bang for your buck will come from PT wood. It is important to sand and seal PT wood right away and not allow it to "weather" any large amount of time unprotected. Although PT wood is rot and decay resistant it is very porous and absorbs water readily, these cycles of absorbing water and drying out cause the open grain to raise and will cause splits if left unsealed. Resent changes to the pressure treating formulas have netted a much nicer looking lumber, now not so green colored, better grades of PT lumber can be quite attractive with natural honey colors and grain showing clearly. But for a high end project where PT just won't do, you must consider other options.

Cedars: Although cedar and redwood are stable and attractive and contain natural oils that make them resistant to insects and rot, they may be too soft for most deck applications, and very pricey to purchase in clear grade (no knots). Redwood and Cypress are increasingly scarce and expensive, while Western Red Cedar remains plentiful. Western Red has been used for siding and roofing as well as decks, and is a very attractive dark red/brown lumber with a lovely scent  as such it is often used in closet linings. Another cedar, Port Orford cedar (sometimes called perfume cedar)harvested in the north west is used in outdoor projects, it is harder then western red but not very stable and very light colored. This aromatic cedar is usually found with many small non stable knots, it is a difficult to stain and does not weather gracefully, especially the knots. Sometimes Alaskan Yellow is used for decks with many of the attributes of Port Orford cedar.

Straight grain fir does not offer much rot and insect resistance and should be consider only in covered porch applications.

The lesser Mahogany's (Red Meranti and Cambara) are viable options but are in the same price range as the denser exotics which will perform better, also the mahogany's have a "speckled" grain which can fill will dirt and mold/mildew. Meranti the Philippine mahogany related to luan is much superior to the lower cost Cambara. Meranti ranges in color and density form the blond unappealing "luan" to the dark red which is denser and much more attractive. The dark red Meranti boards do well outdoors, are resistant to insects and rot weather to a nice silver patina if left unsealed, staining or sealing can be problematic as it is difficult to obtain a long term finish.

Santos mahogany is a beautiful desirable lumber that has become very popular in the interior hard wood floor marketplace as well as in furniture. Not sure if too many Santos mahogany decks are going up

Siberian Larch hearing a lot about this wood now that USSR has collapsed. Look a lot like South Yellow Pine but quite a bit denser, with a tight grain and mostly heartwood, plentiful and sustainable in Russia and can be very fairly priced. Natural resins and density make it very unappealing to insects and decaying fungi. 

The exotics: Tigerwood, Purple Heart, Jarrah, Jatoba, Cumaru, Teak and Ipe: Are all very hard and durable and perform great outdoors! Tigerwood has a similar grain to Mahogany and may share the same problem, however is a beautiful wood to look at. Teak is likely priced out of most peoples budget. Jatoba,Jarrah and Cumaru are all fantastic examples of extreme exotic woods, however ,for the last number of years Ipe is considered the ultimate outdoor lumber and priced competitively with all the other exotics.

Tigerwood  or Goncalo Alves is an atttractive very figured wood, light golden brown with darker colored streaking similar to koa. Some people love the look while others find it too busy. Pricing is very good and the wood is durable, naturally resistant to rot and decay. Getting up there in the Janka scale it going to start to be tougher to cut, fasten and shape but not as extreme as Ipe. This is another wood finding a market in the interior flooring market as well. Again, just be aware at how busy a large area of this wood can became.

Purpleheart Purpleheart so named for its wild purple color which it becomes thru aging and oxidation. The grain is mostly straight but sometimes irregular wavy or interlocking. Heartwood is very resistant to termites and fungi. A dense exotic lumber, although the color is not for everyone. Have not heard as much about availabity lately.

Cumaru is similar in appearance to Ipe, but with a more interlocking grain which makes it less stable, and it does not wear as well and looks less attractive, it can sometimes be confused with a lower grade Ipe and is less costly alternative when overall quality and look are not as important such as a large boardwalk.

 Jatoba Brazilian Cherry is a beautiful tan/salmon wood that will turn burgundy or deep red with orange tones after time. Jatoba has an interlocking grain with medium to course texture. Used extensively for high end interior floors. Jatoba is very dense and durable but maybe better suited to indoors as is difficult to season. If not dried or seasoned slowly may be prone to surface checking, warping and case hardening. Heartwood however,is naturally resistant to insects and decay.

Jarrah Australian another exotic lumber. Jarrah is salmon pink to rich reddish brown and fragrant when fresh, most desirable when it has a straight grain. Old growth has become severely depleted and new growth is a small percentage of available stock, this material may be played out in the US market. Heartwood is highly rot and insect resistant. there is even a wood preservative said to be from Jarrah oil

Ipe The ironwoods are inherently clear, not extremely pricey, but very difficult to work with (Extremely heavy and difficult to cut, screw, nail, or machine).

For the ultimate in durability there is no equal to Ipe (the ironwood). As its nickname implies the wood is tough as iron. Although very difficult to work with, nothing lasts as long outdoors. A rich beautiful wood that ages gracefully to a silver patina if left unfinished