Solid timber. Here we have two choices - Hardwood or softwood. Don't be deceived by the name, some hardwoods are soft such as Balsa wood whereas some softwoods are hard such as Pitch Pine which is as hard as oak!
We shall deal with softwoods first, now for most fretwork softwoods are poor for two reasons - one is that it is not strong and it breaks and chips easily especially on small projections etc and secondly the cut edges tend to be very splintery and will require lots of extra sanding work later. You can cut down on the splintering by using reverse tooth blades (see the page on Blades) or by using a sacrificial layer underneath the work (see the section on Stack cutting).
Softwoods can be used when making thicker items where breakages are less likely such as pull along toys, however, do be aware when making items for children to play in softwood that as mentioned it does suffer from splintering during cutting and is more likely to splinter during play!
Now we come to hardwood. Hardwoods are excellent for fretwork/scrollsaw work for many reasons. Firstly most hardwood is much stronger than most softwood and a lot less prone to breakage - also most people look upon items made from hardwood as better quality especially as far as finish is concerned. When cutting with a fretsaw there is much less splintering than you get with softwood and if you use reverse tooth blades you will often find the edges do not even require sanding.
Generally hardwoods are better for thinner work, once you get to very thick work it becomes very much harder to cut and will blunt blades a lot more quickly. Hardwoods are also more difficult to obtain and cost more to buy, however there is a way around this.
Rather than buy expensive hardwood look out for old discarded furniture that people often throw out and replace with more modern stuff made from MDF! Often old chests of drawers etc have drawers made from quality hardwood even oak. Also ideal are those drawers used in shops for clothing etc they almost always are made of oak and are often an ideal thickness for fretwork. Charity shops are often glad to get rid of old furniture that has been given to them. Every single piece of fretwork I have made is from discarded stuff.