Buying a GBA Flash Cart in 2013

Only reason there is it might be slightly easier to use for holding many games at once. Compatibility wise as long as it is not a supercard, supercard clone (team cyclops made one) or one of the earliest GBA carts (you will be extraordinarily hard pressed to find one of these) then compatibility is the same near 100%* for every flash cart going assuming you can fit it on the cart (the likes of the EZ4 lite compact and M3 Pro series had a small limit as they were aimed at DS games, also some of the earlier carts and more recently the firecards only had 128Mbit where games eventually went up to 256Mbit, there is a bit of note in the 256Mbit world but not as much as most think).

+ the occasional rom hack that uses the extra space


*down the rabbit hole we go.
Trouble games
NES classics and later famicom mini. Patches available if you want but importantly there are emulators in pocketnes and HVCA that offer a superior experience.
If you are curious about what was done to protect them then a full analysis is available
https://mgba.io/2014/12/28/classic-nes/
Dragon Ball (Z?) titles. Some of the other few titles to have AP on the GBA. Patches http://gbatemp.net/threads/log1-2-3-ez-flash-iv.348556/#post-4655532
Yoshi universal gravitation/topsy turvy. Tilt sensor. Patches available http://www.advanscene.com/html/Releases/dbreleases.php?id=1947 http://www.advanscene.com/html/Releases/dbreleases.php?id=2001 http://www.advanscene.com/html/Releases/dbreleases.php?id=1799
Warioware twisted. Tilt sensor. Patches available http://www.advanscene.com/html/Releases/dbreleases.php?id=1979
Koro Koro Puzzle - Happy Panechu!
Tilt sensor
http://www.advanscene.com/html/Releases/dbreleases.php?id=0408
Legendz series. Hardware addon (think spyro skylanders). Unpatched on anything mainly as it is extra hardware that needs sorting, there may be some scope to fix it though.
Plaston/Plastar Gate (Bouken Yuuki Pluster World - Densetsu no PlustoGate and another with EX on the end). Apparently another hardware thing a la legendz above, fixes available for both entries in the series.
http://www.advanscene.com/html/Releases/dbreleases.php?id=1020
http://www.advanscene.com/html/Releases/dbreleases.php?id=2006
Boktai/Solar Boy Django. Solar sensors and RTC.
http://gbatemp.net/threads/boktai-solar-sensor-patch-kit.245127/ (do read the whole thread).
Pokemon games with RTC.
GBATA from http://www.no-intro.org/tools.htm is my preferred patch set/tool here for ruby and sapphire.
For emerald you might try
http://gbatemp.net/threads/any-rtc-...emerald-using-ez-flash-4.354231/#post-4767363
Megaman 4.5 had RTC or something if the people doing patches are to be believed, they should have also sorted that with any patch that arrives.
Top gun combat zones
http://www.advanscene.com/html/Releases/dbreleases.php?id=1906
Others
I have yet to confirm Samurai Deeper Kyo as having AP -- it seems to be an unwinnable first boss.
I think polarium has RTC. Polarium without a touchscreen though.....
Possibly one of the Tony Hawk games has RTC (you set a time at least).
The GBA videos for Shrek (whole films) have now been dumped and as expected used bankswitching. More info https://mgba.io/2015/10/20/dumping-the-undumped/
Likewise I had an interesting discussion a few years back with a guy that had one of those tourist trap 90 in 1 (in reality 5 in one with a lot of cheats/mods) things where they were trying to dump it.

Hardware stuff.
The personal organiser game is probably the most notable and I think it has extra hardware.
Naturally the TV decoders, action replay/gameshark/codebreaker/xploder cheat stuff and the Ereader dumps will not do much of anything without their attendant hardware.
To the best of my knowledge the FM radio stuff was not hardware at all but simply used the GBA as a way to power it and did not speak to it at all.
As you might imagine the glucoboy will need its hardware as I am pretty sure the GBA and/or your chosen flash cart did not come with blood sugar detection hardware built in.

Homebrew. I know you deliberately did not mention it but pogoshell might cause some trouble somewhere as it was designed for certain carts and could exceed the 256Mbit limit. http://kuwanger.altervista.org/gba/pogoshell/ and http://kuwanger.altervista.org/gba/plugin2gba/ should sort that though.
Similarly I am told Flubba's PCE/TG16 emulator could use the extra RAM on the EZ3 to allow PCE-CD emulation. It might also work for the EZ4 but who knows.
Any other homebrew problems are almost always save (fixes/workarounds are readily available) or bad header (fix the header-- http://www.gameboy-advance.net/rom_tools/flash_advance_toolkit.htm and GBATA from http://www.no-intro.org/tools.htm , sometimes combined together, should do that) related.

GBA video. If you are running it on a GB player.
http://www.caitsith2.com/gba_video_arv3.htm has workarounds. Do not run GBA video on a GB player as it will look awful.

Rare exceptions.
A handful of the 256 Mbit titles had some non FF/00 code at the end of it. I trimmed it manually without issue but I later heard that it might have actually been something.

Also trimming.
There were a few GBA games that did not work with GBA style trimming. The solution was do not trim or set a byte or three a couple of dozen bytes after the apparent end of the ROM to something other than 00 or FF and cause the trimmer to stop there and have the game still work.

Odd hacks. Some hacks seem to like changing one of the header bytes to something other than the 00 it is in every known game, my guess was as a flag of some form to prevent a high level editor from editing the game (I have seen such things a few times before).
The EZ4 seemingly uses this 00 as a header detection/end of string affair and if you write it to the NOR then it will not show up. Change it back to 00 and all is right with the world.
I have never seen an emulator only hack for the GBA.

Link issues. Save patching, reset patching and sleep mode type hacks seem to mess up the link timing for some games. Use VBAlink or disable the patching (rather than fiddle with saves you could always stick the unpatched game in a folder with the same name and it will load the appropriate save).

EZ4 specific stuff.
Some games seem to only save (write the save back to the EZ4) if they use 8:3 style naming. Not sure why but it happens and is easily solved by using 8:3 naming.

Gamecube hookups and DS hookups.
Various games for the GC and DS could speak to the GBA (slot) and load stuff from there. Naturally as flash carts patch for SRAM they do not have the flash and EEPROM often used by those games.
For most this means pokemon PAL park and whatever pokemon stadium was called on the GC. The former has a patch ( http://filetrip.net/nds-downloads/rom-hacks/download-pokepatch-42-f27240.html ) and the GC stuff is nowhere to be seen.
More generally the EZ4 kind of had support for DS just needing the game to be present and you could probably work around a lot with the GC if you thought it through. Most GC stuff wanting a hookup just wanted the GBA though.

That is quite literally every edge case I have ever encountered on the GBA, they are so few and far between and largely easily solved that compatibility is up there at that near 100% if you want it to be (give or take quibbles on how well you rate the fixes in the case of the tilt games). This is also why I have to frown at things like the supercard that mess this up.