I currently have 6 scouts, which is the maximum my Board will allow me, without specifically asking for more. At the level of club I am, that seems sufficient. I suppose it depends on the league that you're in, the league rules on foreign players, and your staff budget.
Yeh, it does depend on what league you are in, your transfer budget, where you are allowed to send your scouts etc.
First off, you MUST have a scout to 'scout next opposition'. He needs good TK - Tactical Knowledge and JPA - Judging Player Ability (JPP is irrelevant). his scout reports will help you prepare for your next match if you use them properly.
Now I'm managing a non-league club and i can only scout the UK. I have no transfer budget, so for me one scout scouring for freebies is enough. Actually he's useless and my assman does a better job recommending suitable players, so I send my scout to report on those that the assman flags up.
However, if you're with a big club with big budget, the more regions you can cover the better. Roaming is a good idea too.
I have 4. I am 5 seasons in and have won the league last 2 seasons.
2 are South American based. Both with high Potential Ability ratings.
2 are European based, one with high Potential Ability and the other with high Current Ability.
I would echo what others have said though - have as many as you are allowed. Compared to players they are very cheap and as long as they are constantly scouting good markets you will always have a load of recommendations when you come to need to sign a player.
Always get as many as you're allowed and/or can afford.
I always just set them to scout the world on Roaming because I can't be bothered micro-managing my scouts. I sign them, set them to roam, and can forget about setting new assignments. I also try to sign scouts of various nationalities to take advantage of the knowledge they already have, often even if it means their scouting abilities are poor.
With a major club I have anywhere from 6-8 scouts. The most important 6 scout the nations with the biggest talents and the greatest chances of coming up with superb regens in the future. For me it's usually Argentina, Brazil, France, Germany, Italy, Spain. I have at least one scout based in the region I'm playing in (i.e. England, Spain, etc.) and one that's more "special" either having knowledge of a "rare" area or scouting the next fixture. I set the scouts up so that they constantly monitor all major tournaments: CL, Euro Cup, World Cup, European Championship, South American Cup, etc. The reason for having fewer scouts is that you will generally be winning stuff, advancing to upper levels of CL and so on and you'll have money to buy superstars.
With a mid-level club things get a bit more complicated. With these sort of clubs I bug my board CONSTANTLY for new scouts. In my current game I have 14 scouts. I look for scouts catered to each region, but if I can't find any for a specific region (say South America) I get a good scout and set him to scout the region in a roaming fashion until he gets good at it. The reason behind this set up is because you NEED to scour for players. Finding regens is more important for your team as you might not afford the best of the best. Also there's some brilliant hidden gems in places people don't scout too often (Israel, Middle East, North America) and you'll want to pick those up.
When you're a lower league club it's pretty much up to the board. I try to ensure I have the best scout possible, I scout the home nation (reduces financial expenses) and that's about it. Money is tight and there's enough talent in your home region for cheap if all you need to do is avoid relegation or get promoted from the Blue Square North.