At nearly any level, Wands remain a viable source of hp damage healing. A Wand of Cure Light Wounds heals 275 points of HP for 750gp on average, is scalable to most wounds, and has an action usage of 'Out of Combat'.
Combined with a few scrolls of things like Remove Disease, Remove Curse, Restoration, at higher levels another wand of Lesser Restoration, it's the 3.5 answer to 'no-one wanted to play a cleric', provided a sufficient quantity of Use Magic Device to activate.
In Non-Core, a Wand of Lesser Vigor cures 550 hp at that same 'Out of Combat' speed. Other options, like Faith Healing, possibly have some in-combat utility (assuming everyone worships the same god).
Potions don't require a Use Magic Device check to activate. They are also absurdly expensive compared to wands and scrolls. That's really it.
Having A Magical Healer
This seems like a no-brainer, but when you have someone who can cast curing spells out of combat (and usually, should only be casting them out of combat), your cheapest and easiest source of healing magic is often them.
However, this comes with an opportunity cost in terms of utility spells and combat spells that go unprepared or uncast in favour of magical healing. Even at high levels, canny spellcasters find uses for lower-level spells, and often the sheer quantity of hp-damage received in high level encounters will burn out all the low level spell slots of even a slightly optimized healer.
As such, other than the 'Dedicated Healer' concept, most healers in 3.5 that i've seen.. carry wands. They might have the occasional spell slot for a Break Enchantment or Restoration, but even Lesser Restoration usually shows up in wand form - when you get hit by Shadows, a Lesser to restore everyone strength-drained is usually all your 2nd level spell slots.
As such, other than a bit of extra utility and the occasional in-combat heal, a well stocked healing box of wands and scrolls and someone with Use Magical Device is basically the same as a healer, in that regard.
Consequences: Due to the way WBL scales, you are generally going to be able to heal HP damage. More esoteric stuff might need to wait a day, or a trip to the local church, but i've never seen a party get into trouble running out of healing even when i've done my damnedest to wear them down. And really, you don't want them to, because low-hp means you suddenly need to lowball encounters to a frankly embarrassing extent.
With just Wands, it relies on there being healers who craft healing supplies in the setting, but in most DnD settings this is a fairly safe assumption. Break Enchantment is the highest level 'needed' out of combat healing spell, and it's 5th - depending on setting, it might be hard to find scrolls of this, and with CL issues, if you have a party wizard or sorcerer it's better for them to cast it.
Overall: It works, it's cheap, except in no-magic settings.
High Op/High Level Solutions
Another technique i've seen used for out of combat in higher level or higher op games i've run was to Persist (Persistent Spell) a Lesser Vigor or Mass Lesser Vigor spell, giving an individual or the group effectively Fast Healing 1 for 24 hours. It removed any hp healing requirements out of combat, and even better, all hp book-keeping. It just became a matter of 'how many rounds passed' since the last combat, if they managed to get in a fight before they'd certainly be fully healed.
Consequences/Overall: Works well if you have a character who can cast it, and unlike other Persistent Spell shenanigans I have seen, no-one ever complains about it. The removal of book-keeping alone is a godsend.
On Dispel: Surprisingly large amounts of legitimate encounters do not have access to Dispel or Greater Dispel Magic. And that's fine! Targeting encounters specifically to target powerful elements of the group or tactics the group uses should be something only intelligent enemies with intelligence on the PCs should use - if every Joe, Dick and Sally does it, the GM is a) cheating b) a dick.
The Vitality Point/Wound Point system (from Unearthed Arcana) is absolutely amazing. It allows you to have an actual HP system that tracks how many 'hits' a character can take before they actually get screwed over without constantly being covered in cuts and bites and whatnot from monster claws, have actual 'oh no, blah is grievously hurt and can't move!' moments, makes critical hits suddenly meaningful in the HP-rich world of 'Beyond 3rd Level', and is just wonderful and great.
The sole area where it falls down is that you only recover 1 Vitality Point per Hour. I houseruled it personally to Character Level in vitality points per minute, for a High Action game (what I think of typical DnD as), and Character Level in Vitality per Hour for a Gritty game (think Western movie, or Deadlands).
Consequences: With the Houserule, magical healing became this thing you hoarded against necessary situations like actual Wound Point loss or serious badnasty fixes. I got to be much rougher with the party in general, which I enjoyed. The 'Healer' became a lot more important to the party in general, rather than being treated like a hp packdonkey and an expected amenity. It was generally magical and wonderful and you should use it forever.
The Boom/Bust of Healing
Generally I find that you either need a LOT of healing, or you need very little. Either your tactics are good and you finish off the encounter without taking much damage, or you get pasted and burn through spells like children eating chocolates, which puts you in bad shape for the next encounter and so forth.
Also often encounters seem to naturally flow in groups of hard/soft so the Boss Lair of Evil is going to wipe the floor with you, but the mostly investigatory Ninja Assassin Guild is going to leave you relatively unscathed (or vice versa).
This is hell on Healers or Eternal Wands or whatever that deliver their healing per day, since some days you need 1000 points of hp healing and 36 points of ability damage and 8 doses of poison and 5 diseases, and some days you need like, 50.
Worse, Healers have to use those spell slots in battles that are going south, so they have even less to spend on healing afterwards. That's why competent healers often carry a wand even if they try to use slots for healing. For that 'overflow' healing when the party is having a bad day (or runs into a mission with a Time factor that means you can't stop to get spells back). It's why, in my opinion, Wands or some source of nigh-infinite healing is generally a good thing to have on you.
Realism and Wounds
Stab wounds are pretty painful. Most times, people don't want to have them. Having a stab wound is really terrible and GMs who play HP-As-Wounds and then characters walk around with huge wounds and ignore them makes me sad.
Something to take into account with wounds and magical healing is that realistically people would want to have their wounds fully healed as soon as possible - so 'waiting' until someone has 'enough' wounds to cast a Heal on them or something is really weird conceptually.
People can and will waste resources to not have to feel horrible pain.
So any consideration of out of combat healing should take that into account. If people are roleplaying, they won't want to walk around at half-HP with wounds.
Touch of Healing and Draconic Aura: Vigor
Some people tout Touch of Healing/Dragon Shaman as a healer replacement, as it can keep people filled to half-hp all day with no resource expenditure whatsoever. This is false. The resource you are expending is your hitpoints, to wit, half of them at all times. Having half-hp means you get KO'd easier, affected by more of the symbol line of spells, and have to fight more cautiously, all of which can easily snowball. In practice, low starting HP is the highest source of TPKs I have witnessed. Only in games where the GM regularly lowballs fights and they are at worst trivially difficult can a group rely on Touch of Healing.
If you can get it cheaply, though (and probably not at the cost of a feat - feats are expensive), it can save you on some wand charges.