I do the same thing. Where I have the option, on border cities I'll farm the tile closest to the border and cottage on the interior tiles. The other thing that sucks about border tiles in border cities is when they culture flip. If the AI's going to steal my tiles, it's going to be a farm, not a town.
It also helps to farm tiles outside fat crosses that are near borders. Sure, it might give the AI a bit of cash, but they'll usually stop to pillage instead of marching right to your city - if the AI gets fifty gold but I have time to bring in reinforcements, I'm happy.
They'd have to pillage 12 farms to get 50 gold, at a minimum of 12 turns they give you to prepare a defense. That's a lot of culture-push to outside the fat cross, although with creative leaders I've sometimes had a good culture spread.
At a minimum I road and/or railroad all the border tiles because very nearly all the AIs stop to whack roads, and they get no pillage gold from it--just slows them down artificially.
What's funny is when I have an oil tile in the border lands because no matter how impregnable a defensive stack I have on that tile: mech infantry, marines, tanks, gunships, etc., an attacker like Montezuma will expend every possible unit he can to try to get to that tile for pillage until he's down to 1 or 2 cavs weakened to 0.5 strength and they run off elsewhere for easier pillaging, in which case then my Marines clean 'em up. As someone said before, the AIs don't have any sort of a reasonable set of war tactics, and I've found the biggest difference between losing and winning, is simply knowing how the AIs fight wars, and anticipating that "doctrine" with a counter-strategy:
1. They have priorities on what they want to pillage, and will completely wipe out nearly all of their attacking force to try to get to that 5 to 10 gold they get from it, or to deny you a resource like iron, oil, horses, etc., depending on the era. Good defense of those tiles, even with a large stack of obsolete units (which in your zone just saves you maintenance if you lose 'em in battle), goes a tremendously long way toward wearing even the strongest of opponents down in their onslaught.
2. They almost never use siege weaponry to wear down defenses to zero. They will (foolishly) attack a city with their stack after only one or two wear-downs of city defense. I've often found having more than one strong defender unit is over-redundant, because combined with city defense modifiers, often a single Longbow defending a city on a hill can wipe out 4 or 5 Knights as they rush at the walls. When I draft or whip or otherwise rush a defense together to counter a stack of doom heading for a city, I calculate for a 1:3 ratio of strong defender units against their strongest attacking units. Then a 1:2 ratio of specialist defenders or counterattack units (e.g., Pikes, Maces) versus their appropriate target units (cavalry, melée, et al) With ratios like that a city can hold, without whipping or drafting or depleting the overall defensive unit pool beyond that level.
3. On defense, the AIs will swarm the first approaching stack to a city with half of the siege weapons (cats, cannons, artillery) they have, and hang the rest of them back for... forever, LOL. To counter this counterattack I try to send a smaller "scout" stack to my siege location (forest-hill, forest, hill, or on top of a vital resource or Town, in that order of preference, depending on what options there are in the avenue of approach), and even if the scout stack gets wiped out by a muscular defense, the main stack will be met with MUCH lighter resistance, and the bombardment of the defenses can go on as planned.
4. When an AI attempt to take a city fails, they don't learn from it. They keep on trying and trying, sometimes forever, and even when they pick a new city to attack later, it's often with the same techniques, the same mix of units--which usually isn't very mixed at all, but normally very heavy on cavalry and a small amount of artillery, the counter for which is anti-cav units (pikes, rifles, etc.) and a small amount of cavalry. Just enough artillery to slightly soften up the stacks.
5. As mentioned above, usually the AI has one particular of what I call a "rely upon" unit, that is, about 90% of its production will be of that unit. For the Japanese it'll be Samurai in the appropriate era. For most of them when the Cavalry unit is relatively new they'll "rely" on that one--NO MATTER HOW MANY RIFLEMEN YOU HAVE, which means easy warfare if you have West Point and Heroic Epic in a high-prod city cranking out rifles with Combat II and Formation. They pick up zero clue from this that it's time to change up the attacking units a bit. Even rifles with just Combat II from non-WP cities have better than even chances of beating down Cavalry, and even 2 Pikes per Cav are good odds if you haven't gotten to Rifling yet. Anyway, the predictability here gets just plain ridiculous after a point.
All in all I've found it best just to be prepared to shift to a wartime footing, rather than have tons of units "showing force" at the borders to prevent an invasion. BRING THEM ON, and when they do, their attacking units get obliterated, their WW skyrockets, their production falters, and they only have minor farm- and mine-plunders to show for all the losses. Often these idiots are offering peace before I even have my offensive stack built from my queue-swaps, such is the devastation they encounter on attack. And it's not over for them until "all their cities are belong to us", for that continent anyway. Methodical, patient, clever war strategy just takes one city after another, and the only real challenge to it is keeping the economic infrastructure and cultural improvements whipped up to be able to "digest" all that massive conquest, the ability to absort a large number of cities in as short a time period as it can be done. And even there the conquest process itself helps out in the plunder amount given for taking cities. Even if at the end of a continental blitz my slider's down to 30% due to the massive influx of city upkeep, WW unhappies, 4 or 5 cities still in Resistance mode, tiles pillaged, and all the other overall economic damage that war brings, that's still 30% of a LOT of cities, so tech advancement doesn't slow down near as much as I initially feared in my earlier games. As I've played more I've become less shy about just keeping the conquest on the march, and don't worry about the freakin' slider until the post-war Rebuilding Phase.
IMO. Other people's mileage may vary.
have me leaning on the mouse almost exclusively.
); at least I didn't notice it occur any. If true, that would mean that once it decimated a tile that such a tile would then be immune to further damage even if it were a tile that could be improved slightly again. Then again, I could be wrong and any improvement may re-attract it again, but I would imagine the programmer would make the desert terrain very low priority on the strikes even if it wouldn't prove immune. So the lesson could be, if you play long enough, every single non-city or non-water tile could be destroyed down to desert level, and therefore it could appear that the strikes had stopped altogether at one point, but unfortunately that would be for lack of targets and not that it got any better. 
